UNIVERSITÀ DEGLI STUDI DI PARMA DIPARTIMENTO DI INGEGNERIA INDUSTRIALE

CORSO DI LAUREA MAGISTRALE IN INGEGNERIA MECCANICA

CARATTERIZZAZIONE DELL’AMBIENTE TERMICO SEMICONFINATO DALLA NUOVA COPERTURA IN VETRO

IN PIAZZA GHIAIA A PARMA: CONFRONTO TRA RISULTATI ANALITICI E SPERIMENTALI

THERMAL ENVIRONMENTAL CHARACTERIZATION OF THE

NEW GLASS COVERED SEMI-OUTDOOR SPACE IN GHIAIA

SQUARE, PARMA: COMPARISON BETWEEN ANALYTICAL

AND EXPERIMENTAL RESULTS

Relatore:

Chiar.mo Prof. Ing. GIORGIO PAGLIARINI

Correlatori:

Ph.D. Ing. CARLO CORRADI

Ph.D. Ing. PAMELA VOCALE

Tesi di laurea di:

FILIPPO FONTANESI

Anno Accademico 2011/2012

I

■♥tr♦❞✉③✐♦♥❡

P✐❛③③❛ ●❤✐❛✐❛ è ✉♥❛ ♣✐❛③③❛ st♦r✐❝❛ ❞✐ ✐♠♣♦rt❛♥③❛ ♠♦♥✉♠❡♥t❛❧❡ ❡ ❝♦♠♠❡r❝✐❛❧❡ ❞✐ P❛r✲

♠❛✳ ❙❡❞❡ ❞✐ ♠❡r❝❛t✐ ✜♥ ❞❛✐ t❡♠♣✐ ❞✐ ▼❛r✐❛ ▲✉✐❣✐❛✱ ♥❡❧ ❞♦♣♦❣✉❡rr❛ ❧❛ ♣✐❛③③❛ ❤❛ ♠❛♥t❡♥✉t♦

q✉❡st❛ s✉❛ ❝❛r❛tt❡r✐st✐❝❛ ❞✐ ♠❡r❝❛t♦✱ ♣❛r❛❣♦♥❛❜✐❧❡ ❛ P✐❛③③❛ ❞❡❧❧❡ ❊r❜❡ ❛ ❱❡r♦♥❛ ♦ ❛ ❈❛♠♣♦

❞❡✬ ❋✐♦r✐ ❛ ❘♦♠❛✳ ❖❧tr❡ ❝❤❡ ♠❡r❝❛t♦✱ ❡r❛ ♣✉♥t♦ ❞✐ ❛❣❣r❡❣❛③✐♦♥❡✱ s♦♣r❛tt✉tt♦✱ ♠❛ ♥♦♥ s♦❧♦✱

♣❡r ♠♦❧t✐ ❛♥③✐❛♥✐ ❛❜✐t✉❛t✐ ❛❞ ✏❛♥❞❛r❡ ✐♥ ●❤✐❛✐❛✑ q✉♦t✐❞✐❛♥❛♠❡♥t❡ ❛ ❢❛r❡ s♣❡s❛ ✈❡♥❡♥❞♦ ❞❛

t✉tt✐ ✐ q✉❛rt✐❡r✐ ❞✐ P❛r♠❛✳

❖❣❣✐ ❧❛ ♣✐❛③③❛ ♥♦♥ è ♣✐ù ♣✉❜❜❧✐❝❛✱ ♠❛ è st❛t❛ ❝♦♥❝❡ss❛ ❞❛❧ ❈♦♠✉♥❡ ✐♥ ❣❡st✐♦♥❡ ❛❞ ✉♥ ❝♦♥✲

s♦r③✐♦ ❞✐ ♣r✐✈❛t✐ ❝❤❡ ❤❛♥♥♦ r✐q✉❛❧✐✜❝❛t♦ ❧✬❛r❡❛ ❡ ♠♦❞✐✜❝❛t♦ ❛r❝❤✐t❡tt♦♥✐❝❛♠❡♥t❡ ❧❛ ♣✐❛③③❛✱

❝♦♥❢❡r❡♥❞♦❧❡ ❝❛r❛tt❡r✐st✐❝❤❡ ♣❛r❛❣♦♥❛❜✐❧✐ ❛❞ ✉♥ ♠♦❞❡r♥♦ ❝❡♥tr♦ ❝♦♠♠❡r❝✐❛❧❡ ❝♦♥ ♥❡❣♦③✐✱

♠❛ ❛♥❝❤❡ ❝♦♥ ❛tt✐✈✐tà r✐❝r❡❛t✐✈❡ ❝♦♠❡ r✐st♦r❛♥t✐ ❡ ❝❛✛è ✉❜✐❝❛t✐ ❛❧❧✬❛♣❡rt♦✳ P❡r ❝♦♥tr♦❧❧❛✲

r❡ ❡ ♠✐t✐❣❛r❡ ❧❡ ✈❛r✐❛③✐♦♥✐ ♠✐❝r♦❝❧✐♠❛t✐❝❤❡ ❞✐ ✉♥ ❛♠❜✐❡♥t❡ ♥♦♥ ❝♦♥✜♥❛t♦✱ P✐❛③③❛ ●❤✐❛✐❛

è st❛t❛ ❞♦t❛t❛ ❞✐ ✉♥ s✐st❡♠❛ ❞✐ ❝♦♣❡rt✉r❛ ✐♥ ✈❡tr♦ s✉♣♣♦rt❛t❛ ❞❛ tr❛✈❛t✉r❡ ♠❡t❛❧❧✐❝❤❡❀

q✉❡st❛ str✉tt✉r❛ ❢✉♥❣❡ ❞❛ r✐♣❛r♦ ❞❛❧❧✬❛♠❜✐❡♥t❡ ❡st❡r♥♦ s❡♥③❛ ❛tt❡♥✉❛r❡ ❡❝❝❡ss✐✈❛♠❡♥t❡ ❧❛

❧✉♠✐♥♦s✐tà ♥❛t✉r❛❧❡✱ r❡♥❞❡♥❞♦ ✉t✐❧✐③③❛❜✐❧❡ ❧✬❛r❡❛ ❛❞ ❛tt✐✈✐tà ❝♦♠♠❡r❝✐❛❧✐✱ t✐♣♦ ♠❡r❝❛t✐♥✐ ❛

t❡♠❛✱ ♠❛♥✐❢❡st❛③✐♦♥✐ ❞✐ ✈❛r✐♦ ❣❡♥❡r❡✱ ♣❡r q✉❛s✐ t✉tt♦ ❧✬❛♥♥♦✳

✶

■♥ s❡❞❡ ❞✐ ♣r♦❣❡tt❛③✐♦♥❡ s✐ è st❛❜✐❧✐t❛ ✉♥❛ ❝♦♥✈❡♥③✐♦♥❡ ❞✐ r✐❝❡r❝❛ tr❛ ❯♥✐✈❡rs✐tà ❞❡❣❧✐ ❙t✉❞✐

❞✐ P❛r♠❛ ❡ Pr♦❣❡tt♦ ●❤✐❛✐❛ s✳r✳❧✳ ✭❝♦♥s♦r③✐♦ ❞✐ ♣r✐✈❛t✐ ❝♦♥❝❡ss✐♦♥❛r✐✮ ♣❡r ❝♦♥❞✉rr❡ ✉♥✬❛♥❛✲

❧✐s✐ ❞❡❧❧❡ ❛❧t❡r❛③✐♦♥✐ ❛♠❜✐❡♥t❛❧✐ ❡ ❞❡❧❧❡ ❝♦♥❞✐③✐♦♥✐ ❞✐ ❝♦♠❢♦rt ❛♠❜✐❡♥t❛❧❡ ❛ss♦❝✐❛t❡ ❛❧ ♥✉♦✈♦

s✐st❡♠❛ ❞✐ ❝♦♣❡rt✉r❛✳ ■♥ ♣❛rt✐❝♦❧❛r❡ ✐❧ ❣r✉♣♣♦ ❞✐ ❧❛✈♦r♦ ❞❡❧ ❉✐♣❛rt✐♠❡♥t♦ ❞✐ ■♥❣❡❣♥❡r✐❛

■♥❞✉str✐❛❧❡✱ ❝♦♦r❞✐♥❛t♦ ❞❛❧ Pr♦❢✳■♥❣✳●✳P❛❣❧✐❛r✐♥✐✱ s✐ è ♦❝❝✉♣❛t♦ ❞❡❧❧✬✐♠♣❧❡♠❡♥t❛③✐♦♥❡ ❞✐ ✉♥

♠♦❞❡❧❧♦ ♥✉♠❡r✐❝♦ ♣❡r ❧❛ s✐♠✉❧❛③✐♦♥❡ ❞❡❧❧❡ ❝♦♥❞✐③✐♦♥✐ ♠✐❝r♦❝❧✐♠❛t✐❝❤❡ ❛✐ ✜♥✐ ❞❡❧❧❛ ✈❡r✐✜❝❛

❞❡❧❧❡ ❝♦♥❞✐③✐♦♥✐ ❞✐ ❝♦♠❢♦rt t❡r♠♦✐❣r♦♠❡tr✐❝♦ ❛❧❧✬✐♥t❡r♥♦ ❞❡❧❧❛ ③♦♥❛ ❞❡❧❧❛ ❝♦♣❡rt✉r❛✱ ❞❡❧❧✬❛✲

♥❛❧✐s✐ ❝r✐t✐❝❛ ❞❡✐ r✐s✉❧t❛t✐ ♦tt❡♥✉t✐ ♥❡❧❧❡ ❞✐✈❡rs❡ ♦r❡ ❞❡❧ ❣✐♦r♥♦ ❡ ♥❡✐ ❞✐✈❡rs✐ ♣❡r✐♦❞✐ ❞❡❧❧✬❛♥♥♦

❡ ❞❡❧❧✬✐♥❞✐✈✐❞✉❛③✐♦♥❡ ❞✐ ❡✈❡♥t✉❛❧✐ str❛t❡❣✐❡ ❞✐ ♠✐t✐❣❛③✐♦♥❡ ❞❡❧❧❡ ❝♦♥❞✐③✐♦♥✐ ❛♠❜✐❡♥t❛❧✐✳

P❡r ❧❛ ✈❛❧✐❞❛③✐♦♥❡ ❞❡❧ ♠♦❞❡❧❧♦ ♥✉♠❡r✐❝♦ ❡ ❧❛ ✈❡r✐✜❝❛ ❞❡❧❧❡ ❛ss✉♥③✐♦♥✐ ✐♠♣✐❡❣❛t❡✱ è st❛t❛ ❝♦♥✲

❞♦tt❛ ✉♥❛ ❝❛♠♣❛❣♥❛ ❞✐ ♠✐s✉r❡ ✐♥ s✐t✉ ❛♥❝❤❡ ❛✈✈❛❧❡♥❞♦s✐ ❞✐ str✉♠❡♥t❛③✐♦♥✐ s♣❡❝✐✜❝❤❡ ♣❡r

❧❛ ✈❛❧✉t❛③✐♦♥❡ ❞❡✐ ♣❛r❛♠❡tr✐ ♠✐❝r♦❝❧✐♠❛t✐❝✐❀ ♣❡r ❧❛ ❞❡✜♥✐③✐♦♥❡ ❞❡❧❧❡ ❝♦♥❞✐③✐♦♥✐ ❛❧ ❝♦♥t♦r♥♦

❞❡❧ ♠♦❞❡❧❧♦✱ s♦♥♦ st❛t✐ ✉t✐❧✐③③❛t✐ ❞❛t✐ ❝❧✐♠❛t✐❝✐ ♦r❛r✐ r✐❧❡✈❛t✐ ❞❛ ❆❘P❆ ✭❆❣❡♥③✐❛ ❘❡❣✐♦♥❛❧❡

Pr❡✈❡♥③✐♦♥❡ ❡ ❆♠❜✐❡♥t❡ ❞❡❧❧✬❊♠✐❧✐❛ ❘♦♠❛❣♥❛✮ ❡ ❞❛t✐ r❡❧❛t✐✈✐ ❛❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ r✐❧❡✈❛t✐

✐♥ ❧♦❝♦✳

▲❛ ❝❛♠♣❛❣♥❛ ❞✐ ♠✐s✉r❡✱ ❧❛ t❛r❛t✉r❛ ❞❡✐ ♣❛r❛♠❡tr✐✱ ♣❛rt❡ ❞❡❧❧❛ ♠♦❞❡❧❧❛③✐♦♥❡ ❡ ❧❛ s✐♠✉❧❛③✐♦♥❡

❝♦♥t❡st✉❛❧✐③③❛t❛ ♥❡✐ ❣✐♦r♥✐ ❡ ♥❡❧❧❡ ♦r❡ ❞❡❧❧❡ ♣r♦✈❡ s♣❡r✐♠❡♥t❛❧✐✱ ✐❧ ❝♦♥❢r♦♥t♦ tr❛ ❧❡ ♣r❡✈✐s✐♦♥✐

❡ ✐ ❞❛t✐ r✐❧❡✈❛t✐✱ ❡ ❧✬❛♥❛❧✐s✐ ❝r✐t✐❝❛ ❞❡✐ r✐s✉❧t❛t✐ s♦♥♦ ♦❣❣❡tt♦ ❞❡❧ ♣r❡s❡♥t❡ ❧❛✈♦r♦ ❞✐ t❡s✐✳

✷

✶ ▲✉♦❣♦ ♦❣❣❡tt♦ ❞✐ ✐♥❞❛❣✐♥❡

P✐❛③③❛ ●❤✐❛✐❛ è ✉❜✐❝❛t❛ ♥❡❧ ❝❡♥tr♦ st♦r✐❝♦ ❞✐ P❛r♠❛✱ ❞❡❧✐♠✐t❛t❛ ❛❞ ❊st ❞❛❧ ▲✉♥❣♦

P❛r♠❛ ✭r✐✈❛ ❞❡str❛ ❞❡❧ t♦rr❡♥t❡ ♦♠♦♥✐♠♦✮ ❡ ❞❛❧❧❡ ❛♥t✐❝❤❡ ❇❡❝❝❤❡r✐❡✱ ❛ ❙✉❞ ❞❛❧❧✬❛♥t✐❝❛ ✈✐❛

❊♠✐❧✐❛✱ ❛❞ ❖✈❡st ❞❛ ♣❛❧❛③③✐ ❞✬❡♣♦❝❛ ❡❞ ❛ ◆♦r❞ ❞❛❧ ❝♦♠♣❧❡ss♦ ♠♦♥✉♠❡♥t❛❧❡ ❞❡❧❧❛ P✐❧♦tt❛✳ ■❧

♣✐❛♥♦ ❝❛❧♣❡st❛❜✐❧❡ ❞❡❧❧❛ ♣✐❛③③❛ s✐ tr♦✈❛ ❛❞ ✉♥ ❧✐✈❡❧❧♦ ✐♥❢❡r✐♦r❡ ❞✐ ❝✐r❝❛ ❝✐♥q✉❡ ♠❡tr✐ r✐s♣❡tt♦

❧❡ q✉♦t❡ ❛❞ ❊st ❡ ❛ ❙✉❞ ❡❞ è r❛❣❣✐✉♥❣✐❜✐❧❡ tr❛♠✐t❡ s❝❛❧✐♥❛t❡✳ ❆❧ ❞✐ s♦tt♦ ❞❡❧❧❛ ♣✐❛③③❛ è

st❛t♦ r❡❛❧✐③③❛t♦ ✉♥ ♣✐❛♥♦ ❞❡❞✐❝❛t♦ ❛ ♥❡❣♦③✐ ❡❞ ❛tt✐✈✐tà ❝♦♠♠❡r❝✐❛❧✐ ❡ ❞✉❡ ♣✐❛♥✐ ❛ ♣❛r❝❤❡❣❣✐♦

♣r✐✈❛t♦✳

❋✐❣✉r❛ ✶✳✶✿ ❱✐st❛ ❛❡r❡❛ ❞❡❧ s✐st❡♠❛ ❞✐ ❝♦♣❡rt✉r❛ ❞✐ P✳③③❛ ●❤✐❛✐❛✱ P❛r♠❛

▲❛ r✐q✉❛❧✐✜❝❛③✐♦♥❡ ❣❡♥❡r❛❧❡ ❞❡❧❧✬❛r❡❛ ❤❛ ✐♥s❡r✐t♦ ✉♥ ♥✉♦✈♦ s✐st❡♠❛ ❞✐ ❝♦♣❡rt✉r❛✱ ♠♦str❛t♦

✐♥ ❋✐❣✉r❛ ✶✳✶✱ ❝❤❡ s✐ s✈✐❧✉♣♣❛ ✐♥ tr❡ ❡❧❡♠❡♥t✐ ✈❡tr❛t✐ ❞✐s❣✐✉♥t✐ ✐rr❡❣♦❧❛r✐ ❛ ♣r♦✜❧♦ ❝✉r✈♦

♣❡r ✉♥ t♦t❛❧❡ ❞✐ 3500 m2✱ s✉♣♣♦rt❛t✐ ❞❛ ✉♥❛ str✉tt✉r❛ ♠❡t❛❧❧✐❝❛ r❡❛❧✐③③❛t❛ ❞❛ ❝♦❧♦♥♥❡ ❛

s❡③✐♦♥❡ ❝✐r❝♦❧❛r❡ r❛♠✐✜❝❛t❡ ❝❤❡ s♦st❡♥❣♦♥♦ tr❛✈✐ ♣r✐♥❝✐♣❛❧✐ ❝♦♥t✐♥✉❡ ❛❞ ❛♥❞❛♠❡♥t♦ ❝✉r✈♦✱

s✉❧❧❡ q✉❛❧✐ ♣♦❣❣✐❛♥♦ tr❛✈✐ s❡❝♦♥❞❛r✐❡ r❡tt✐❧✐♥❡❡✳

▲❛ ♣✐❛♥t❛ è ❛ ❢♦r♠❛ ❞✐ q✉❛❞r✐❧❛t❡r♦✱ ❝♦♥ ✐ ❧❛t✐ ♠❛❣❣✐♦r✐✱ ✐♥ ❞✐r❡③✐♦♥❡ ❧♦♥❣✐t✉❞✐♥❛❧❡✱ ❛✈❡♥t✐

❧✉♥❣❤❡③③❛ ❞✐ ❝✐r❝❛ 120 m✱ ❡❞ ✐ ❞✉❡ ♠✐♥♦r✐✱ ✐♥ ❞✐r❡③✐♦♥❡ tr❛s✈❡rs❛❧❡✱ ❛✈❡♥t✐ ❧✉♥❣❤❡③③❛ ❞✐

❝✐r❝❛ 11 m ❡ 35 m✳

✸

▲❛ s✉♣❡r✜❝✐❡ ❞✐ ❝♦♣❡rt✉r❛ ♣r❡s❡♥t❛ ♣❡♥❞❡♥③❛ ✈❛r✐❛❜✐❧❡ ❝❤❡ ❞❡t❡r♠✐♥❛ ✉♥❛ ✈❛r✐❛③✐♦♥❡ ❞✐

q✉♦t❛ ♠❛ss✐♠❛ ❞✐ ❝✐r❝❛ 4 m✳ ■ tr❡ ❞✐st✐♥t✐ ❡❧❡♠❡♥t✐ ❝❤❡ ❧❛ ❝♦♠♣♦♥❣♦♥♦ s✐ s✉ss❡❣✉♦♥♦✱ ✉♥♦

❞♦♣♦ ❧✬❛❧tr♦✱ ✐♥ ❞✐r❡③✐♦♥❡ ❧♦♥❣✐t✉❞✐♥❛❧❡ ❝♦♥ ✉♥ ❛♥❣♦❧♦ ❞✐ ✐♥❝❧✐♥❛③✐♦♥❡ ❞✐ ❝✐r❝❛ 5◦ r✐s♣❡tt♦

❛❧❧❛ s✉♣❡r✜❝✐❡ ♦r✐③③♦♥t❛❧❡ ✭❋✐❣✉r❛ ✶✳✷ ✮✳

❋✐❣✉r❛ ✶✳✷✿ ❙❡③✐♦♥❡ ❧♦♥❣✐t✉❞✐♥❛❧❡ ❞❡❧❧❛ ❝♦♣❡rt✉r❛

▲❛ ❝♦♣❡rt✉r❛ è st❛t❛ r❡❛❧✐③③❛t❛ ✉t✐❧✐③③❛♥❞♦ ❧❛str❡ q✉❛❞r❛t❡ ✐♥ ❝r✐st❛❧❧♦ str❛t✐✜❝❛t♦ ❞✐ s✐✲

❝✉r❡③③❛ ❙❊❘❊❳✱ ❞✐ ❞✐♠❡♥s✐♦♥✐ 1.45 m × 1.45 m✱ ❛✣❛♥❝❛t❡ ✐♥ ♠♦❞♦ ❞❛ ♦tt❡♥❡r❡ ✉♥❛

s✉♣❡r✜❝✐❡ ❝♦♥t✐♥✉❛ ❛❞❛tt❛ ❛❞ ❡ss❡r❡ s♦rr❡tt❛ ❞❛❧❧❛ str✉tt✉r❛ ♣♦rt❛♥t❡✳ ▲❡ ❧❛str❡ ✐♥ ✈❡tr♦

❤❛♥♥♦ ✉♥♦ s♣❡ss♦r❡ ❞✐ 19.52 mm ❡ ❧❡ ❝❛r❛tt❡r✐st✐❝❤❡ ❡♥❡r❣❡t✐❝❤❡ ❞✐❝❤✐❛r❛t❡ ❞❛❧ ❝♦str✉tt♦r❡

s♦♥♦ r✐♣♦rt❛t❡ ✐♥ ❚❛❜❡❧❧❛ ✶✳✶ s❡❝♦♥❞♦ ♥♦r♠❛ ❊◆ ✹✶✵ ✲ ✷✵✵✶ ❬✷✺❪✳ ■♥ ✉♥❛ ③♦♥❛ ❧✐♠✐t❛t❛

❞❡❧❧❛ ❝♦♣❡rt✉r❛ s♦♥♦ st❛t❡ ✐♥s❡r✐t❡✱ ❛❧❧✬✐♥t❡r♥♦ ❞❡❧❧❡ ❧❛str❡ ❞✐ ✈❡tr♦✱ ❞❡❧❧❡ ❝❡❧❧❡ ❢♦t♦✈♦❧t❛✐❝❤❡

♣❡r ❧❛ ♣r♦❞✉③✐♦♥❡ ❞✐ ❡♥❡r❣✐❛ ❡❧❡ttr✐❝❛✳

■♥♦❧tr❡ ❛❧tr❡ ❧❛str❡ s♦♥♦ st❛t❡ ❛rr✐❝❝❤✐t❡ ❞❛ s❡r✐❣r❛✜❡ ❝❤❡ r✐❝❤✐❛♠❛♥♦ ❧❛ ❢♦r♠❛ ❞❡❧❧❡ ❝❡❧❧❡

❢♦t♦✈♦❧t❛✐❝❤❡✱ s✐❛ ♣❡r ❛✉♠❡♥t❛r❡ ❧✬❡✛❡tt♦ ❞✐ s❝❤❡r♠❛t✉r❛ ❞❡❧❧✬❡♥❡r❣✐❛ s♦❧❛r❡ ❡♥tr❛♥t❡✱ s✐❛ ♣❡r

❛❧❧❡❣❡r✐r❡ ❧✬✐♠♣❛tt♦ ✈✐s✐✈♦ ❞❡❧❧❡ ❝❡❧❧❡ ❢♦t♦✈♦❧t❛✐❝❤❡✳ ▲❡ s❡r✐❣r❛✜❡ ♣r❡s❡♥t❛♥♦ s❝❤❡r♠❛t✉r❡

❞✐✈❡rs❡✱ ✐♥ ❢✉♥③✐♦♥❡ ❞❡❧ ❣r❛❞♦ ❞✐ ♦s❝✉r❛♠❡♥t♦ ✈♦❧✉t♦✿ ✐♥ ❋✐❣✉r❛ ✶✳✸ ✈✐ s♦♥♦ r❛♣♣r❡s❡♥t❛t✐

❞✉❡ t✐♣✐ ❞✐ s❡r✐❣r❛✜❡ ❛♣♣❧✐❝❛t❡ s✉❧❧❡ ❧❛str❡ ❞✐ ✈❡tr♦✳

■♥ ❚❛❜❡❧❧❛ ✶✳✷ è r✐♣♦rt❛t♦ ✐❧ ❣r❛❞♦ ❞✐ ❛ss♦r❜✐♠❡♥t♦ ♣❡r ♦❣♥✐ t✐♣♦ ❞✐ ❧❛str❛ ❞✐ ✈❡tr♦✿ s✐❛ ♣❡r

q✉❡❧❧❡ ❝♦♥ ❧❡ ❝❡❧❧❡ ❢♦t♦✈♦❧t❛✐❝❤❡✱ s✐❛ ♣❡r q✉❡❧❧❡ ❝♦♥ ✐ ❞✐✈❡rs✐ t✐♣✐ ❞✐ s❡r✐❣r❛✜❡✱ s✐❛ ♣❡r q✉❡❧❧❡

♣r✐✈❡ ❞✐ s❡r✐❣r❛✜❛❀ ✐♥♦❧tr❡ ✈✐ è s♣❡❝✐✜❝❛t♦ ✐❧ ♥✉♠❡r♦ ❞✐ ❧❛str❡ ❝❤❡ s♦♥♦ st❛t❡ ♠♦♥t❛t❡ ✐♥

❝♦♣❡rt✉r❛ ♣❡r ♦❣♥✐ ❞✐✈❡rs❛ t✐♣♦❧♦❣✐❛✳

✹

❊◆ ✹✶✵ ✲ ✷✵✶✶

❚r❛s♠✐ss✐♦♥❡ ❡♥❡r❣❡t✐❝❛ (te) 59.6

❘✐✢❡ss✐♦♥❡ ❡♥❡r❣❡t✐❝❛ ❡st❡r♥❛(re) 6.3

❘✐✢❡ss✐♦♥❡ ❡♥❡r❣❡t✐❝❛ ✐♥t❡r♥❛(re) 6.3

❆ss♦r❜✐♠❡♥t♦ ❡♥❡r❣❡t✐❝♦ (ae) 34.1

❋❛tt♦r❡ s♦❧❛r❡ (g) 67.7

❈♦❡✣❝✐❡♥t❡ ❞✐ ♦♠❜r❡❣❣✐❛♠❡♥t♦ (sc) 0.78

❚r❛s♠✐ss✐♦♥❡ ❞✐ r❛❣❣✐ ✉❧tr❛✈✐♦❧❡tt✐ (UV ) 0

❚❛❜❡❧❧❛ ✶✳✶✿ ❈❛r❛tt❡r✐st✐❝❤❡ ❡♥❡r❣❡t✐❝❤❡ ❞❡❧ ✈❡tr♦ ❞✐ ❝♦♣❡rt✉r❛

✭❛✮ ✭❜✮

❋✐❣✉r❛ ✶✳✸✿ ❊s❡♠♣✐ ❞✐ s❡r✐❣r❛✜❡✿ ✭❛✮ t✐♣♦ ✶❀ ✭❜✮ t✐♣♦ ✸

■♥ ❋✐❣✉r❛ ✶✳✹ è r❛♣♣r❡s❡♥t❛t♦ ✐❧ ❞✐s❡❣♥♦ ❝♦♠♣❧❡ss✐✈♦ ❞❡❧❧❛ ❝♦♣❡rt✉r❛ ❡❞ ✐❧ ♣♦s✐③✐♦♥❛✲

♠❡♥t♦ ❞❡❧❧❡ ❞✐✈❡rs❡ t✐♣♦❧♦❣✐❡ ❞❡❧❧❡ ❧❛str❡ s♦♣r❛❝✐t❛t❡✿ ✐♥ ❜✐❛♥❝♦ s♦♥♦ ✐♥❞✐❝❛t❡ ❧❡ ❧❛str❡ ✐♥

✈❡tr♦ ♥♦♥ s❡r✐❣r❛❢❛t♦✱ ✐♥ ❜❧✉ ❧❡ ❧❛str❡ ❝♦♥ s❡r✐❣r❛✜❛ t✐♣♦ ✶✱ ✐♥ ❣r✐❣✐♦ ❧❡ ❧❛str❡ ❝♦♥ s❡r✐❣r❛✜❛

t✐♣♦ ✷✱ ✐♥ ♥❡r♦ ❧❡ ❧❛str❡ ❝♦♥ s❡r✐❣r❛✜❛ t✐♣♦ ✸ ❡❞ ✐♥ ❛③③✉rr♦ ❧❡ ❧❛str❡ ❝♦♥ s❡r✐❣r❛✜❛ t✐♣♦ ✹✳

■♥♦❧tr❡✱ s✐ ♣✉ò ♥♦t❛r❡ ❝❤❡ ❧❡ ❝❡❧❧❡ ❢♦t♦✈♦❧t❛✐❝❤❡ s♦♥♦ ♣♦s✐③✐♦♥❛t❡ ♥❡❧❧❛ ③♦♥❛ ❝❡♥tr❛❧❡ ❞❡❧❧❛

❝♦♣❡rt✉r❛ ✭❣r✐❣✐♦ s❝✉r♦✮✳

✺

◆✳ ❧❛str❡ ❝♦♣❡rt✉r❛ ❆ss♦r❜✐♠❡♥t♦ ❛❞❞✐③✐♦♥❛❧❡ %

❈❡❧❧❡ ❢♦t♦✈♦❧t❛✐❝❤❡ 83 63

❙❡r✐❣r❛✜❛ t✐♣♦ ✶ 107 34

❙❡r✐❣r❛✜❛ t✐♣♦ ✷ 134 22

❙❡r✐❣r❛✜❛ t✐♣♦ ✸ 196 15

❙❡r✐❣r❛✜❛ t✐♣♦ ✹ 414 15

❱❡tr♦ ✲ 0

❚❛❜❡❧❧❛ ✶✳✷✿ ●r❛❞♦ ❞✐ ❛ss♦r❜✐♠❡♥t♦ ❞❡❧❧❡ ❧❛str❡ ❞✐ ✈❡tr♦

❋✐❣✉r❛ ✶✳✹✿ ❉✐str✐❜✉③✐♦♥❡ ❧❛str❡ ✐♥ ✈❡tr♦

✻

■❧ ❜❛s❛♠❡♥t♦ s♦tt♦ ❧❛ ❝♦♣❡rt✉r❛ ❝♦♥st❛ ✉♥❛ s♦❧❡tt❛ ♠✉❧t✐✲str❛t♦ ❞✐ s♣❡ss♦r❡ ❝♦♠♣❧❡ss✐✈♦

♣❛r✐ ❛ 91 cm ✭❋✐❣✉r❛ ✶✳✺✮✱ t✉tt❛✈✐❛ ♥♦♥ t✉tt♦ ❧♦ s♣❡ss♦r❡ ❞❡❧❧❛ s♦❧❡tt❛ è ✐♥t❡r❡ss❛t♦ ❞❛❧

tr❛♥s✐t♦r✐♦ t❡r♠✐❝♦ ✐♥❞♦tt♦ ❞❛❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ❝❤❡ ❝♦❧♣✐s❝❡ ✐❧ ♣❛✈✐♠❡♥t♦✿ s♦♥♦ st❛t✐✱

✐♥ ♣❛rt✐❝♦❧❛r❡✱ ❝♦♥s✐❞❡r❛t✐ s♦❧♦ ✐ ♣r✐♠✐ q✉❛ttr♦ str❛t✐ ❞❡❧ pacchetto ❞✐ ♣❛✈✐♠❡♥t❛③✐♦♥❡✱ ♣❡r

✉♥♦ s♣❡ss♦r❡ ❝♦♠♣❧❡ss✐✈♦ ❞✐ 30 cm✱ ✐♥❞✐✈✐❞✉❛♥❞♦ ✉♥ ❝♦♥✜♥❡ ❛❞✐❛❜❛t✐❝♦ ✐♥ ❝♦rr✐s♣♦♥❞❡♥③❛

❞❡❧ sottofondo alleggerito✳ ▲✬❡q✉❛③✐♦♥❡ ❞✐ ❋♦✉r✐❡r ♣❡r ✐❧ ❝❛❧❝♦❧♦ ❞❡❧ tr❛♥s✐t♦r✐♦ t❡r♠✐❝♦

è st❛t❛ r✐s♦❧t❛ s❡♣❛r❛t❡♠❡♥t❡ ♣❡r ❝✐❛s❝✉♥♦ ❞❡✐ q✉❛ttr♦ str❛t✐ ❝♦♥s✐❞❡r❛t✐✳ ■♥ ❚❛❜❡❧❧❛ ✶✳✸

s♦♥♦ r✐♣♦rt❛t❡ ❧❡ ♣r♦♣r✐❡tà ❞❡✐ ♠❛t❡r✐❛❧✐ ❝❤❡ ❝♦st✐t✉✐s❝♦♥♦ ✐❧ ❜❛s❛♠❡♥t♦ s❡❝♦♥❞♦ ♥♦r♠❛

❯◆■ ✶✵✸✺✶ ✲ ✶✾✾✹ ❬✷✹❪✳

❋✐❣✉r❛ ✶✳✺✿ P❛❝❝❤❡tt♦ ❞✐ ♣❛✈✐♠❡♥t❛③✐♦♥❡ ❞❡❧❧❛ ♣✐❛③③❛

❉❡♥s✐tà (kg/m3) ❈❛❧♦r❡ s♣❡❝✐✜❝♦ (J/kgK) ❈♦♥❞✳ t❡r♠✐❝❛ (W/mK✮

P♦r✜❞♦ 2200 840 2.90

▼❛❧t❛ 2000 840 1.40

❈❛❧❝❡str✉③③♦ 2200 840 1.48

❆❧❧❡❣❣❡r✐t♦ 700 840 0.42

❚❛❜❡❧❧❛ ✶✳✸✿ Pr♦♣r✐❡tà ❞❡✐ ♠❛t❡r✐❛❧✐ ❝♦st✐t✉❡♥t✐ ✐❧ ❜❛s❛♠❡♥t♦

✼

✷ ▼♦❞❡❧❧♦ ❞✐ ❝❛❧❝♦❧♦

■❧ ♠♦❞❡❧❧♦ ❞✐ ❝❛❧❝♦❧♦ ♣❡r ❧✬❛♠❜✐❡♥t❡ s❡♠✐✲❝♦♥✜♥❛t♦ ♦❣❣❡tt♦ ❞✐ ✐♥❞❛❣✐♥❡ ❢❛ r✐❢❡r✐♠❡♥✲

t♦ ❛❧❧❛ s❡③✐♦♥❡ tr❛s✈❡rs❛❧❡ ❞❡❧❧❛ str✉tt✉r❛ ❡✈✐❞❡♥③✐❛t❛ ✐♥ ❋✐❣✉r❛ ✷✳✶ ❡ s❝❤❡♠❛t✐❝❛♠❡♥t❡

r✐♣♦rt❛t❛ ✐♥ ❋✐❣✉r❛ ✷✳✷✳

❋✐❣✉r❛ ✷✳✶✿ P✐❛♥t❛ ❞❡❧❧❛ ❝♦♣❡rt✉r❛ ✭❞❛ ❇✉✐❧❞✐♥❣ Pr♦❥❡❝t✱ ✇✇✇✳❜✉✐❧❞✐♥❣♣r♦❥❡❝t✳✐t✱ ✷✵✵✾✮

▲♦ s❝❤❡♠❛ ❝♦♥s✐st❡ ✐♥ ✉♥♦ str❛t♦ ❞✐ ❛r✐❛ ❝♦♠♣r❡s♦ tr❛ ❧❛ ❝♦♣❡rt✉r❛ ✐♥ ✈❡tr♦✱ ❛ss✉♥t❛

❝♦♠❡ ✉♥❛ ❧❛str❛ ❝♦♥t✐♥✉❛ ❞✐ s♣❡ss♦r❡ ❝♦st❛♥t❡ ✐♥❝❧✐♥❛t❛ ❞✐ ✉♥ ❛♥❣♦❧♦ α = 5◦ r✐s♣❡tt♦

❧✬♦r✐③③♦♥t❛❧❡ ❡❞ ✐❧ ❜❛s❛♠❡♥t♦ ❝❤❡ ❝♦st✐t✉✐s❝❡ ✉♥❛ ❝❛♣❛❝✐tà t❡r♠✐❝❛ ❞✐str✐❜✉✐t❛ ❝♦♠♣r❡♥❞❡♥t❡

❛♥❝❤❡ ❧✬❡✛❡tt♦ ❞❡❣❧✐ ❡❧❡♠❡♥t✐ str✉tt✉r❛❧✐✳ ▲❛ ❧❛r❣❤❡③③❛ è L = 36 m✱ ❧✬❛❧t❡③③❛ ♠✐♥✐♠❛ è

H1 = 4.5 m ❡ s✐ ❛ss✉♠❡ ❝❤❡ ♥♦♥ ✈✐ s✐❛ ❛❧❝✉♥ ❝♦♥✜♥❛♠❡♥t♦ s✉ ❡♥tr❛♠❜✐ ✐ ❧❛t✐✳ ■♥♦❧tr❡

❝♦♥s✐❞❡r❛♥❞♦ ❧❛ ❧✉♥❣❤❡③③❛ ❞❡❧❧❛ ❝♦♣❡rt✉r❛✱ ✐♥ ❞✐r❡③✐♦♥❡ ♥♦r♠❛❧❡ ❛❧❧❛ ❋✐❣✉r❛ ✷✳✷✱ ❡ss❡r❡

✐♥✜♥✐t❛✱ è ♣♦ss✐❜✐❧❡ ❛✛r♦♥t❛r❡ ✐❧ ♣r♦❜❧❡♠❛ ♥❡❧❧✬ ✐♣♦t❡s✐ ❞✐ ♠♦♥♦❞✐♠❡♥s✐♦♥❛❧✐tà✳

▲❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ✐♥❝✐❞❡♥t❡ s✉❧❧❛ ❝♦♣❡rt✉r❛ è ✐♥ ♣❛rt❡ r✐✢❡ss❛✱ ✐♥ ♣❛rt❡ ❛ss♦r❜✐t❛ ❞❛❧

✈❡tr♦ ❡❞ ✐♥ ♣❛rt❡ tr❛s♠❡ss❛ ♥❡❧❧♦ s♣❛③✐♦ s♦tt♦st❛♥t❡ ❞♦✈❡ ✈✐❡♥❡ ✐♥ ♣❛rt❡ ❛ss♦r❜✐t❛ ❡❞ ✐♥

♣❛rt❡ r✐✢❡ss❛ ❞❛❧ ❜❛s❛♠❡♥t♦✳ ■❧ ❝♦♥s❡❣✉❡♥t❡ r✐s❝❛❧❞❛♠❡♥t♦ ❞❡❧ ♣❛✈✐♠❡♥t♦ ❣❡♥❡r❛ ✉♥ ✢✉ss♦

❝♦♥✈❡tt✐✈♦ ♥❛t✉r❛❧❡ ❞✐ ❛r✐❛ ❛ttr❛✈❡rs♦ ❧❡ ❛♣❡rt✉r❡ ❧❛t❡r❛❧✐ ❛♥❝❤❡ ❢❛✈♦r✐t♦ ❞❛❧❧✬✐♥❝❧✐♥❛③✐♦♥❡

❞❡❧❧❛ ❝♦♣❡rt✉r❛✳ ■❧ ♠♦❞❡❧❧♦ r✐s♦❧✈❡ ❧❡ ❡q✉❛③✐♦♥✐ ❞✐ ❜✐❧❛♥❝✐♦ ❞❡❧❧✬❡♥❡r❣✐❛ ♣❡r ❧❛ ❝♦♣❡rt✉r❛✱

♣❡r ✐❧ ✈♦❧✉♠❡ ❞✬❛r✐❛ ✐♥t❡r♥♦ ❡ ♣❡r ✐❧ ❜❛s❛♠❡♥t♦✳

✽

❋✐❣✉r❛ ✷✳✷✿ ❙❡③✐♦♥❡ ❞✐ r✐❢❡r✐♠❡♥t♦ ❆✲❆

■❧ ✈♦❧✉♠❡ ❞✬❛r✐❛ ✐♥t❡r♥♦ è s❝❤❡♠❛t✐③③❛t♦ ❛ ♣❛r❛♠❡tr✐ ❝♦♥❝❡♥tr❛t✐✱ ♠❡♥tr❡ s✐❛ ♣❡r ❧❛ ❝♦✲

♣❡rt✉r❛ ✐♥ ✈❡tr♦ ❝❤❡ ♣❡r ✐❧ ❜❛s❛♠❡♥t♦ s✐ ♣r♦✈✈❡❞❡ ❛❧❧❛ r✐s♦❧✉③✐♦♥❡ ❞❡❧ tr❛♥s✐t♦r✐♦ t❡r♠✐❝♦✱

t❡♥❡♥❞♦ ❝♦♥t♦ ❞❡❧❧❛ ✈❛r✐❛③✐♦♥❡ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ♥❡✐ ❞✐✈❡rs✐ str❛t✐✳

▲❛ ♣r♦❝❡❞✉r❛ ❞✐ ❝❛❧❝♦❧♦ r✐❝❤✐❡❞❡ ✐♥ ✐♥❣r❡ss♦ ✐♥❢♦r♠❛③✐♦♥✐ ❝❧✐♠❛t✐❝❤❡ ✐♥ ❢✉♥③✐♦♥❡ ❞❡❧ t❡♠♣♦✿

• ❚❡♠♣❡r❛t✉r❛ ❞❡❧❧✬❛r✐❛ ❞❡❧❧✬❛♠❜✐❡♥t❡ ❡st❡r♥♦✱ To❀

• ●r❛❞♦ ✐❣r♦♠❡tr✐❝♦ ❞❡❧❧✬❛r✐❛ ❞❡❧❧✬❛♠❜✐❡♥t❡ ❡st❡r♥♦✱ ϕo❀

• ❱❡❧♦❝✐tà ❞❡❧❧✬❛r✐❛ ❞❡❧❧✬❛♠❜✐❡♥t❡ ❡st❡r♥♦✱ Va❀

• ❚❡♠♣❡r❛t✉r❛ ❞❡❧❧❛ ✈♦❧t❛ ❝❡❧❡st❡ ❛❧❧✬✐♥✜♥✐t♦✱ Tsky❀

• ❘❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ❞✐r❡tt❛ ❡ ❞✐✛✉s❛ ✐♥❝✐❞❡♥t❡ s✉❧❧❛ ❝♦♣❡rt✉r❛✱ IT,b ❡ IT,d❀

• ❆♥❣♦❧♦ ❞✐ ✐♥❝✐❞❡♥③❛ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ❞✐r❡tt❛✱ θ❀

• ❱❡❧♦❝✐tà ❞❡❧❧✬❛r✐❛ ❞❡❧❧✬❛♠❜✐❡♥t❡ s❡♠✐✲❝♦♥✜♥❛t♦✱ W ✳

■♥♦❧tr❡ è ♥❡❝❡ss❛r✐♦ ❢♦r♥✐r❡ ❧❡ ♣r♦♣r✐❡tà ❞❡❧ ✈❡tr♦ ❡♠✐s❢❡r✐❝❤❡ ❡❞ ✐♥ ❢✉♥③✐♦♥❡ ❞❡❧❧✬❛♥❣♦❧♦ ❞✐

✐♥❝✐❞❡♥③❛ ❡ ❧❡ ♣r♦♣r✐❡tà ❞❡✐ ❞✐✈❡rs✐ str❛t✐ ❝❤❡ ❝♦st✐t✉✐s❝♦♥♦ ✐❧ ❜❛s❛♠❡♥t♦✳ ❆❧ ✜♥❡ ❞✐ ♦tt❡♥❡r❡

❧❛ ❚❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡ ♦❝❝♦rr❡ ❝❛❧❝♦❧❛r❡ ✐ ❢❛tt♦r✐ ❞✐ ❢♦r♠❛ ❞❡❧❧❡ s✉♣❡r✜❝✐ r✐s♣❡tt♦

❛❧❧❛ ♣❡rs♦♥❛ ✐♥ ♣✐❡❞✐ ❛❧ ❝❡♥tr♦ ❞❡❧❧♦ s♣❛③✐♦ ❡ s♣❡❝✐✜❝❛r❡ ❧❡ ♣r♦♣r✐❡tà r❛❞✐❛t✐✈❡ ❞❡❧ ❝♦r♣♦

✉♠❛♥♦✳

✾

✷✳✶ ❇✐❧❛♥❝✐♦ ❞❡❧❧✬❡♥❡r❣✐❛ ♣❡r ❧❛ ❝♦♣❡rt✉r❛ ✐♥ ✈❡tr♦

■❧ ❜✐❧❛♥❝✐♦ ❞❡❧❧✬❡♥❡r❣✐❛ ♣❡r ❧❛ ❝♦♣❡rt✉r❛ ✐♥ ✈❡tr♦ è ❡s♣r✐♠✐❜✐❧❡ ❛ttr❛✈❡rs♦ ❧✬❡q✉❛③✐♦♥❡

❞✐ ❋♦✉r✐❡r✿

ρgcg∂T r

∂τ=

λg∂2T r

∂x2+

qg,rdg

✭✷✳✶✮

❞♦✈❡ x è ❧❛ ❝♦♦r❞✐♥❛t❛ s♣❛③✐❛❧❡ ♥♦r♠❛❧❡ ❛❧❧❛ ❝♦♣❡rt✉r❛ ❞✐ s♣❡ss♦r❡ dg ❡❞ ✐❧ t❡r♠✐♥❡ ✏❣❡♥❡✲

r❛t✐✈♦✑ qg,r r❛♣♣r❡s❡♥t❛ ❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ❛ss♦r❜✐t❛✿

qg,r = ar,bIT,b + ar,dIT,d +ar,brm

1− rr,drm(tr,bIT,b + tr,dIT,d) ✭✷✳✷✮

❙✐ ♦ss❡r✈❛ ❝❤❡ ♥♦♥ t✉tt❛ ❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ tr❛s♠❡ss❛ ❛ttr❛✈❡rs♦ ✐❧ ✈❡tr♦ ✈✐❡♥❡ ❛ss♦r❜✐✲

t❛ ❞❛❧ ❜❛s❛♠❡♥t♦✱ ♠❛ ✉♥❛ ❝❡rt❛ ❢r❛③✐♦♥❡ ✈✐❡♥❡ r✐✢❡ss❛ ❞❛❧❧♦ st❡ss♦ ❜❛s❛♠❡♥t♦ ❡ ♣♦✐ ✐♥

♣❛rt❡ ❛ss♦r❜✐t❛ ❞❛❧❧❛ ❝♦♣❡rt✉r❛✳ ■❧ ❝♦❡✣❝✐❡♥t❡ ❞✐ r✐✢❡ss✐♦♥❡ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ♣❡r ✐❧

❜❛s❛♠❡♥t♦✱ rm✱ è ❛ss✉♥t♦ ♣❛r✐ ❛ 0.25 ✐♥❞✐♣❡♥❞❡♥t❡♠❡♥t❡ ❞❛❧❧✬❛♥❣♦❧♦ ❞✐ ✐♥❝✐❞❡♥③❛✳

▲❛ ❝♦♣❡rt✉r❛ s❝❛♠❜✐❛ ❝❛❧♦r❡ ❝♦♥ ❧✬❛♠❜✐❡♥t❡ ❡st❡r♥♦✿

qo = hc,o(Tr,o − To) + hr,o(Tr,o − Tsky) ✭✷✳✸✮

❡ ❝♦♥ ❧✬❛♠❜✐❡♥t❡ s❡♠✐✲❝♦♥✜♥❛t♦✿

qi = hc,i(Tr,i − Ti) + hr,i(Tr,i − Tm) ✭✷✳✹✮

■❧ ❝♦❡✣❝✐❡♥t❡ ❞✐ ❝♦♥✈❡③✐♦♥❡ tr❛ ❧❛ s✉♣❡r✜❝✐❡ ❡st❡r♥❛ ❞❡❧❧❛ ❝♦♣❡rt✉r❛ ❡ ❧✬❛r✐❛ ❛♠❜✐❡♥t❡

❡st❡r♥❛✱ hc,o✱ ❡ ✐❧ ❝♦❡✣❝✐❡♥t❡ ❞✐ ❝♦♥✈❡③✐♦♥❡ tr❛ ❧❛ s✉♣❡r✜❝✐❡ ✐♥t❡r♥❛ ❞❡❧❧❛ ❝♦♣❡rt✉r❛ ❡ ❧✬❛r✐❛

❞❡❧❧✬❛♠❜✐❡♥t❡ s❡♠✐✲❝♦♥✜♥❛t♦✱ hc,i✱ s♦♥♦ st❛t✐ ✈❛❧✉t❛t✐ ✐♠♣✐❡❣❛♥❞♦ ❧✬❡s♣r❡ss✐♦♥❡ ✐♥tr♦❞♦tt❛

❞❛ ❘✳❉✳ ❈❧❡❛r ❡t ❛❧✳ ❬✹❪ ♣❡r s✉♣❡r✜❝✐ ♦r✐③③♦♥t❛❧✐ ❡ s✉❜✲♦r✐③③♦♥t❛❧✐ ❝❤❡ ❝♦♠❜✐♥❛ ❧✬❡✛❡tt♦

❞✐ ❝♦♥✈❡③✐♦♥❡ ❢♦r③❛t❛ ❞♦✈✉t❛ ❛❧ ✈❡♥t♦ ❡ ❣❧✐ ❡✛❡tt✐ ❞❡✐ ✢✉ss✐ ❝♦♥✈❡tt✐✈✐ ✐♥❞♦tt✐ ❞❛❧❧❡ ❢♦r③❡

❞✐ ❣❛❧❧❡❣❣✐❛♠❡♥t♦✳ ◗✉❡st♦ ♠❡t♦❞♦ ❞✐ ❝❛❧❝♦❧♦ ❛❣❣✐✉♥❣❡ ❛✐ r✐s✉❧t❛t✐ ♦tt❡♥✉t✐ ❝♦♥ ❧❡ ♥♦t❡

❡s♣r❡ss✐♦♥✐ ♣❡r ❝♦♥✈❡③✐♦♥❡ ❢♦r③❛t❛ s✉ s✉♣❡r✜❝✐ ♣✐❛♥❡ ❬✶✶❪✱ ✐❧ ❝♦♥tr✐❜✉t♦ ❞❡❧❧❛ ❝♦♥✈❡③✐♦♥❡

✶✵

♥❛t✉r❛❧❡ ✏♣❡s❛t♦✑ s✉ ✉♥ ❢❛tt♦r❡ ❝❤❡ ✈❛ ❛ ③❡r♦ ♦ ❛❞ ✉♥♦ ♣❡r ✈❛❧♦r✐✱ r✐s♣❡tt✐✈❛♠❡♥t❡✱ ♠♦❧t♦

❜❛ss✐ ♦ ♠♦❧t♦ ❛❧t✐ ❞❡❧ r❛♣♣♦rt♦ Gr/Re2✳ ▲❡ ❧✉♥❣❤❡③③❡ ❝❛r❛tt❡r✐st✐❝❤❡ ❛ss✉♥t❡ s♦♥♦ L ♣❡r ❧❛

❝♦♥✈❡③✐♦♥❡ ❢♦r③❛t❛✱ L/2 ♣❡r ❧❛ ❝♦♥✈❡③✐♦♥❡ ♥❛t✉r❛❧❡ ❡ s✐ ❝♦♥s✐❞❡r❛ tr❛s❝✉r❛❜✐❧❡ ❧✬❡✛❡tt♦ ❞❡❧❧❛

s❝❛❜r❡③③❛ s✉♣❡r✜❝✐❛❧❡✳ ▲❛ ✈❡❧♦❝✐tà ❞❡❧ ✈❡♥t♦ ♥❡❧❧✬❛♠❜✐❡♥t❡ ❡st❡r♥♦ ❡ ❧❛ ✈❡❧♦❝✐tà ❞❡❧❧✬❛r✐❛

♥❡❧❧♦ s♣❛③✐♦ s❡♠✐✲❝♦♥✜♥❛t♦✱ ✐♠♣✐❡❣❛t❡ ♥❡❧ ❝❛❧❝♦❧♦ ❞❡✐ ❝♦❡✣❝✐❡♥t✐ ❞✐ ❝♦♥✈❡③✐♦♥❡✱ s♦♥♦ ♦t✲

t❡♥✉t❡✱ r✐s♣❡tt✐✈❛♠❡♥t❡✱ ❞❛ ♠✐s✉r❛③✐♦♥✐ ❡✛❡tt✉❛t❡ ❞❛ ❆❘P❆ ❡ ❞❛ ♠✐s✉r❛③✐♦♥✐ str✉♠❡♥t❛❧✐

❡✛❡tt✉❛t❡ ✐♥ ❧♦❝♦✳

■❧ ❝♦❡✣❝✐❡♥t❡ ❞✐ s❝❛♠❜✐♦ t❡r♠✐❝♦ ♣❡r ✐rr❛❣❣✐❛♠❡♥t♦ tr❛ ❧❛ s✉♣❡r✜❝✐❡ ❡st❡r♥❛ ❞❡❧❧❛ ❝♦♣❡rt✉r❛

❡ ❧❛ ✈♦❧t❛ ❝❡❧❡st❡✱ hr,o✱ è ❡s♣r✐♠✐❜✐❧❡ ❝♦♠❡✿

hr,o =σ0(T

2

r,o + T 2

sky)(Tr,o + Tsky)

1/εr + 1/εsky − 1✭✷✳✺✮

❡❞ ✐❧ ❝♦❡✣❝✐❡♥t❡ ❞✐ s❝❛♠❜✐♦ t❡r♠✐❝♦ ♣❡r ✐rr❛❣❣✐❛♠❡♥t♦ tr❛ ❧❛ s✉♣❡r✜❝✐❡ ✐♥t❡r♥❛ ❞❡❧❧❛

❝♦♣❡rt✉r❛ ❡ ❧❛ s✉♣❡r✜❝✐❡ ❞❡❧ ❜❛s❛♠❡♥t♦✱ hr,i✿

hr,i =σ0(T

2

r,i + T 2

m)(Tr,i + Tm)

1/εr + 1/εm − 1✭✷✳✻✮

❙✐ ❝♦♥s✐❞❡r❛♥♦ ❧❛ ❝♦♣❡rt✉r❛ ❡❞ ✐❧ ❜❛s❛♠❡♥t♦ ❝♦♠❡ ❝♦r♣✐ ❣r✐❣✐ ❝♦♥ ✉♥❛ ❡♠✐ss✐✈✐tà ❡♠✐s❢❡r✐❝❛

❞✐ 0.9✱ ♠❡♥tr❡ ❧❛ ✈♦❧t❛ ❝❡❧❡st❡ s✐ ❝♦♠♣♦rt❛ ❝♦♠❡ ✉♥ ❝♦r♣♦ ♥❡r♦ ❛❧❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧ ❝✐❡❧♦

❛❧❧✬✐♥✜♥✐t♦✳

❉❡✜♥✐t❡ ❧❡ ❝♦♥❞✐③✐♦♥✐ ❛❧ ❝♦♥t♦r♥♦✱ ❧❛ s♦❧✉③✐♦♥❡ ♥✉♠❡r✐❝❛ ❞❡❧❧✬❡q✉❛③✐♦♥❡ ❞✐ ❋♦✉r✐❡r ♥❡❧ ✈❡tr♦

è ❛✛r♦♥t❛t❛ ❝♦♥ ✐❧ ♠❡t♦❞♦ ❡s♣❧✐❝✐t♦ ❛❧❧❡ ❞✐✛❡r❡♥③❡ ✜♥✐t❡ s✉❞❞✐✈✐❞❡♥❞♦ ❧♦ s♣❡ss♦r❡ ✐♥ ✸ ♥♦❞✐

❝♦♥ ♣❛ss♦ ❞✐ ✐♥t❡❣r❛③✐♦♥❡ ❞✐ ✷ s❡❝♦♥❞✐✳

✶✶

✷✳✷ ❇✐❧❛♥❝✐♦ ❞❡❧❧✬❡♥❡r❣✐❛ ♣❡r ✐❧ ✈♦❧✉♠❡ ❞✬❛r✐❛ ✐♥t❡r♥♦

❙✐ ❝♦♥s✐❞❡r❛ ❧✬❡q✉❛③✐♦♥❡ ❞✐ ❜✐❧❛♥❝✐♦ ❞❡❧❧✬❡♥❡r❣✐❛ ♣❡r ❧♦ str❛t♦ ❞✬❛r✐❛ ❞❡❧❧✬❛♠❜✐❡♥t❡

s❡♠✐✲❝♦♥✜♥❛t♦ ❝♦♠♣r❡s♦ tr❛ ❧❛ ❝♦♣❡rt✉r❛ ❡❞ ✐❧ ❜❛s❛♠❡♥t♦ ♣❡r ✉♥✐tà ❞✐ s✉♣❡r✜❝✐❡✿

ρacaHavdTi

dτ=

hc,iLr

L(Tr,i − Ti) + hc,m(Tm − Ti) +

ρacaVa(To − Ti)

L✭✷✳✼✮

❈♦♥ ✉♥♦ s❝❤❡♠❛ ❛ ♣❛r❛♠❡tr✐ ❝♦♥❝❡♥tr❛t✐✱ ✐❧ ♠♦❞❡❧❧♦ ❞❡t❡r♠✐♥❛ ❧✬❛♥❞❛♠❡♥t♦ ❞❡❧❧❛ t❡♠♣❡✲

r❛t✉r❛ ❞❡❧❧✬❛r✐❛ ✐♥t❡r♥❛ Ti ✐♥ ❢✉♥③✐♦♥❡ ❞❡❧ t❡♠♣♦✳

■❧ ❝♦❡✣❝✐❡♥t❡ ❞✐ ❝♦♥✈❡③✐♦♥❡ tr❛ ❧❛ s✉♣❡r✜❝✐❡ ❞❡❧ ❜❛s❛♠❡♥t♦ ❡ ❧✬❛r✐❛ ✐♥t❡r♥❛✱ hc,m✱ è ✈❛❧✉t❛t♦

❝♦♥ ❧♦ st❡ss♦ ♠❡t♦❞♦ ✐♠♣✐❡❣❛t♦ ♣❡r ✐❧ ❝❛❧❝♦❧♦ ❞✐ hc,o ❡ hc,i✳

■❧ t❡r♠✐♥❡ Va r❛♣♣r❡s❡♥t❛ ❧❛ ✈❡❧♦❝✐tà ❞❡❧ ✢✉ss♦ ❞✬❛r✐❛ ♥❡❧❧✬❛♠❜✐❡♥t❡ s❡♠✐✲❝♦♥✜♥❛t♦ ❞♦✈✉t♦

❛❧❧✬❡✛❡tt♦ ❝♦♠❜✐♥❛t♦ ❞❡❧❧❛ ❞✐✛❡r❡♥③❛ ❞✐ t❡♠♣❡r❛t✉r❛ tr❛ ❧✬❛♠❜✐❡♥t❡ ✐♥t❡r♥♦ ❡❞ ❡st❡r♥♦ ❡❞

✐❧ ✈❡♥t♦✳ ❉❛t❡ ❧❡ ❞✐✣❝♦❧tà ❞✐ ♠♦❞❡❧❧❛③✐♦♥❡ ♣❡r ❧❛ ❞❡t❡r♠✐♥❛③✐♦♥❡ ❞✐ Va✱ ❝❤❡ r✐❝❤✐❡❞❡r❡❜❜❡✱

♦❧tr❡t✉tt♦✱ ❧❛ ❝♦♥♦s❝❡♥③❛ ❞❡tt❛❣❧✐❛t❛ ❞❡❧❧✬❛rr❡❞❛♠❡♥t♦ ✉r❜❛♥♦ ✈❛r✐❛❜✐❧❡ ✐♥ ❢✉♥③✐♦♥❡ ❞❛❧❧❛

❞❡st✐♥❛③✐♦♥❡ ❞✬✉s♦ ❞❡❧❧❛ ♣✐❛③③❛✱ s✐ è ♣r❡❢❡r✐t♦ ✐♠♣✐❡❣❛r❡ ✐❧ ❞❛t♦ ♠✐s✉r❛t♦ s♣❡r✐♠❡♥t❛❧♠❡♥t❡✳

✶✷

✷✳✸ ❇✐❧❛♥❝✐♦ ❞❡❧❧✬❡♥❡r❣✐❛ ♣❡r ✐❧ ❜❛s❛♠❡♥t♦

■❧ ❜✐❧❛♥❝✐♦ ❞❡❧❧✬❡♥❡r❣✐❛ ♣❡r ✐❧ s✐♥❣♦❧♦ str❛t♦ ❞❡❧ ❜❛s❛♠❡♥t♦ è ❡s♣r✐♠✐❜✐❧❡ ❛ttr❛✈❡rs♦

❧✬❡q✉❛③✐♦♥❡ ❞✐ ❋♦✉r✐❡r✿

ρmcm∂Tm

∂τ=

λm∂2Tm

∂x2+

qg,mdm

✭✷✳✽✮

❞♦✈❡ x è ❧❛ ❝♦♦r❞✐♥❛t❛ s♣❛③✐❛❧❡ ♥♦r♠❛❧❡ ❛❧❧♦ str❛t♦ ❞✐ s♣❡ss♦r❡ dm ❡❞ ✐❧ t❡r♠✐♥❡ ✏❣❡♥❡r❛t✐✈♦✑

qg,m r❛♣♣r❡s❡♥t❛ ❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ❛ss♦r❜✐t❛ ❞❛❧ s♦❧♦ str❛t♦ s✉♣❡r✜❝✐❛❧❡✿

qg,m =am

1− rr,drm(tr,bIT,b + tr,dIT,d) ✭✷✳✾✮

■❧ ❝♦❡✣❝✐❡♥t❡ ❞✐ ❛ss♦r❜✐♠❡♥t♦ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ♣❡r ✐❧ ❜❛s❛♠❡♥t♦✱ am, è ❛ss✉♥t♦ ♣❛r✐

❛ 0.75 ✐♥❞✐♣❡♥❞❡♥t❡♠❡♥t❡ ❞❛❧❧✬❛♥❣♦❧♦ ❞✐ ✐♥❝✐❞❡♥③❛✳

■♥♦❧tr❡ ❧♦ str❛t♦ s✉♣❡r✜❝✐❛❧❡ s❝❛♠❜✐❛ ❝❛❧♦r❡ ❝♦♥ ❧✬❛♠❜✐❡♥t❡ s❡♠✐✲❝♦♥✜♥❛t♦✿

qm,i = hc,m(Ti − Tm) + hr,i(Tr,i − Tm) ✭✷✳✶✵✮

P❡r ❝♦♠♣❧❡t❛r❡ ❧❡ ❝♦♥❞✐③✐♦♥✐ ❛❧ ❝♦♥t♦r♥♦ s✐ ✐♥❞✐✈✐❞✉❛ ✉♥ ❝♦♥✜♥❡ ❛❞✐❛❜❛t✐❝♦ ✐♥ ❝♦rr✐s♣♦♥✲

❞❡♥③❛ ❞❡❧❧♦ str❛t♦ ♣✐ù ♣r♦❢♦♥❞♦ ✐♥ ♠❛t❡r✐❛❧❡ ❛❧❧❡❣❣❡r✐t♦✳

P❡r ✐❧ ❝❛❧❝♦❧♦ ❞❡❧ tr❛♥s✐t♦r✐♦ t❡r♠✐❝♦ s✐ ❝♦♥s✐❞❡r❛♥♦ ✐ ♣r✐♠✐ q✉❛ttr♦ str❛t✐ ❞✐ ♣❛✈✐♠❡♥t❛③✐♦♥❡

❡ ❧❡ r❡❧❛t✐✈❡ ♣r♦♣r✐❡tà ❞❡✐ ♠❛t❡r✐❛❧✐ ✭♣♦r✜❞♦ 5 cm✱ ♠❛❧t❛ ❞✐ ❛❧❧❡tt❛♠❡♥t♦ 5 cm✱ ❝❛❧❝❡str✉③③♦

10 cm✱ s♦tt♦❢♦♥❞♦ ❛❧❧❡❣❣❡r✐t♦ 10 cm✮ ♣❡r ✐ q✉❛❧✐ ❧✬❡q✉❛③✐♦♥❡ ❞✐ ❋♦✉r✐❡r è r✐s♦❧t❛ ♥✉♠❡r✐✲

❝❛♠❡♥t❡ ❝♦♥ ✐❧ ♠❡t♦❞♦ ❡s♣❧✐❝✐t♦ ❛❧❧❡ ❞✐✛❡r❡♥③❡ ✜♥✐t❡✳ ■ q✉❛ttr♦ str❛t✐ ❞✐ ♣❛✈✐♠❡♥t❛③✐♦♥❡

s♦♥♦ s✉❞❞✐✈✐s✐ ✐♥✿ 5 ♥♦❞✐ ♣❡r ✐❧ ♣♦r✜❞♦✱ 5 ♥♦❞✐ ♣❡r ❧❛ ♠❛❧t❛ ❞✐ ❛❧❧❡tt❛♠❡♥t♦✱ 10 ♥♦❞✐ ♣❡r

✐❧ ❝❛❧❝❡str✉③③♦ ❡ 10 ♥♦❞✐ ♣❡r ✐❧ s♦tt♦❢♦♥❞♦ ❛❧❧❡❣❣❡r✐t♦❀ ✐❧ ♣❛ss♦ ❞✐ ✐♥t❡❣r❛③✐♦♥❡ è ✜ss❛t♦ ❛ 2

s❡❝♦♥❞✐✳

✶✸

✷✳✹ ❘❛❞✐❛③✐♦♥❡ s♦❧❛r❡

❉✐ s❡❣✉✐t♦ s♦♥♦ ♣r❡s❡♥t❛t❡ ❧❡ ❞❡✜♥✐③✐♦♥✐✱ ❧❡ ❣r❛♥❞❡③③❡ ❢♦♥❞❛♠❡♥t❛❧✐ ❡ ❧❡ r❡❧❛③✐♦♥✐ ❝❤❡

♣❡r♠❡tt♦♥♦ ❞✐ ♦tt❡♥❡r❡✱ ❛ ♣❛rt✐r❡ ❞❛✐ ❞❛t✐ r✐❧❡✈❛t✐ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ t♦t❛❧❡ s✉ ♣✐❛♥♦

♦r✐③③♦♥t❛❧❡ ♦tt❡♥✉t✐ ❝♦♥ ♠✐s✉r❛③✐♦♥✐ ✐♥ ❧♦❝♦✱ ✐❧ ✈❛❧♦r❡ ❞❡❧❧✬❛♥❣♦❧♦ ❞✐ ✐♥❝✐❞❡♥③❛ θ ❡❞ ✐ ✈❛❧♦r✐

❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ❞✐r❡tt❛✱ IT,b✱ ❡ ❞✐✛✉s❛✱ IT,d✱ s✉❧❧❛ s✉♣❡r✜❝✐❡ ✐♥❝❧✐♥❛t❛ ❞❡❧❧❛ ❝♦♣❡rt✉r❛

✐♥ ❢✉♥③✐♦♥❡ ❞❡❧ t❡♠♣♦ r✐❝❤✐❡st✐ ✐♥ ✐♥❣r❡ss♦ ❞❛❧ ♠♦❞❡❧❧♦ ❞✐ ❝❛❧❝♦❧♦✳

✷✳✹✳✶ ■❧ ❙♦❧❡

■❧ ❙♦❧❡ è ✉♥❛ s❢❡r❛ ❞✐ ♠❛t❡r✐❛ ❣❛ss♦s❛ ♠♦❧t♦ ❝❛❧❞❛ ❝♦♥ ✉♥ ❞✐❛♠❡tr♦ è ❞✐ 1, 39 ·109 m

❡❞ ✉♥❛ ❞✐st❛♥③❛ ♠❡❞✐❛ ❞❛❧❧❛ ❚❡rr❛ ❞✐ 1, 5·1011 m✳ ❱✐st♦ ❞❛❧❧❛ ❚❡rr❛ ✐❧ ❙♦❧❡ r✉♦t❛ ❛tt♦r♥♦

❛❧ s✉♦ ❛ss❡ ❝♦♥ ✉♥ ♣❡r✐♦❞♦ ❞✐ ❝✐r❝❛ q✉❛ttr♦ s❡tt✐♠❛♥❡✳ ▲❛ s✉♣❡r✜❝✐❡ ❞❡❧ ❙♦❧❡ s✐ tr♦✈❛ ❛ ✉♥❛

t❡♠♣❡r❛t✉r❛ ❡✛❡tt✐✈❛ ❞✐ ❝♦r♣♦ ♥❡r♦ ❞✐ 5777 K✳

❋✐❣✉r❛ ✷✳✸✿ ❙tr✉tt✉r❛ ❞❡❧ ❙♦❧❡ ✭❞❛✿ ❏♦❤♥ ❆✳ ❉✉✣❡✱ ❲✐❧❧✐❛♠ ❆✳ ❇❡❝❦♠❛♥✱ ❙♦❧❛r ❊♥❣✐♥❡❡r✐♥❣❚❤❡r♠❛❧ Pr♦❝❡ss♦r✱ ❏♦❤♥ ❲✐❧❡② ✫ ❙♦♥s✱ ■♥❝✳✱ ✶✾✽✵✮

✶✹

■❧ ❙♦❧❡ è ✉♥ r❡❛tt♦r❡ ❛ ❢✉s✐♦♥❡ ❝♦♥t✐♥✉❛ ✐♥ ❝✉✐ ✐ ❣❛s ❝♦st✐t✉❡♥t✐✱ tr❛tt❡♥✉t✐ ❞❛❧❧❡ ❢♦r③❡

❣r❛✈✐t❛③✐♦♥❛❧✐✱ ❢✉♥❣♦♥♦ ❞❛ ❝♦♥t❡♥✐t♦r❡✳ ❚r❛ ❧❡ ♥✉♠❡r♦s❡ r❡❛③✐♦♥✐ ❞✐ ❢✉s✐♦♥❡ ❝❤❡ ❢♦r♥✐s❝♦♥♦

❡♥❡r❣✐❛ ✐rr❛❣❣✐❛t❛ ❞❛❧ ❙♦❧❡✱ q✉❡❧❧❛ ❝♦♥s✐❞❡r❛t❛ ♣✐ù ✐♠♣♦rt❛♥t❡ ❝♦✐♥✈♦❧❣❡ q✉❛ttr♦ ♥✉❝❧❡✐ ❞✐

✐❞r♦❣❡♥♦ ✭♣r♦t♦♥✐✮ ❝❤❡ s✐ ❝♦♠❜✐♥❛♥♦ ♣❡r ❢♦r♠❛r❡ ✉♥ ♥✉❝❧❡♦ ❞✐ ❡❧✐♦❀ ❧❛ ♠❛ss❛ ❞❡❧ ♥✉❝❧❡♦ ❞✐

❡❧✐♦ è ♠✐♥♦r❡ ❞✐ q✉❡❧❧❛ ❞❡✐ q✉❛ttr♦ ♣r♦t♦♥✐✱ t❛❧❡ ❞✐❢❡tt♦ ❞✐ ♠❛ss❛ ❝♦rr✐s♣♦♥❞❡✱ s❡❝♦♥❞♦ ❧❛

❧❡❣❣❡ ❞✐ ❊✐♥st❡✐♥✱ ❛❧❧✬❡♥❡r❣✐❛ ❝♦♥✈❡rt✐t❛✳ ▲✬ ❡♥❡r❣✐❛ ♣r♦❞♦tt❛ ♥❡❧❧❛ ♣❛rt❡ ✐♥t❡r♥❛ ❞❡❧ ❙♦❧❡

❞❡✈❡ ❡ss❡r❡ tr❛s❢❡r✐t❛ ❛❧❧❛ s✉♣❡r✜❝✐❡ ❡ q✉✐♥❞✐ ✐rr❛❣❣✐❛t❛ ♥❡❧❧♦ s♣❛③✐♦✳ ❈✐ò ❛✈✈✐❡♥❡ ❛ttr❛✈❡rs♦

✉♥❛ s✉❝❝❡ss✐♦♥❡ ❞✐ ♣r♦❝❡ss✐ r❛❞✐❛t✐✈✐ ❡ ❝♦♥✈❡tt✐✈✐✱ ❝♦♥ s✉❝❝❡ss✐✈❛ ❡♠✐ss✐♦♥❡✱ ❛ss♦r❜✐♠❡♥t♦

❡ r❡✐rr❛❣❣✐❛♠❡♥t♦✳

■♥ ❋✐❣✉r❛ ✷✳✸ è ♠♦str❛t♦ ✉♥♦ s❝❤❡♠❛ ❞❡❧❧❛ str✉tt✉r❛ ❞❡❧ ❙♦❧❡✳ ❙✐ st✐♠❛ ❝❤❡ ✐❧ 90% ❞❡❧❧✬❡✲

♥❡r❣✐❛ s✐❛ ❣❡♥❡r❛t❛ ♥❡❧❧❛ r❡❣✐♦♥❡ ❝❛r❛tt❡r✐③③❛t❛ ❞❛ ✉♥❛ ❞✐st❛♥③❛ r❛❞✐❛❧❡ ❝♦♠♣r❡s❛ ❢r❛ 0 ❡

0.23 R ✭❞♦✈❡ R è ✐❧ r❛❣❣✐♦ ❞❡❧ ❙♦❧❡✮ ❝❤❡ ❝♦♥t✐❡♥❡ ✐❧ 40% ❞❡❧❧❛ ♠❛ss❛ t♦t❛❧❡✳ ▲❛ s✉♣❡r✜❝✐❡

❛♣♣❛r❡ ❝♦♠♣♦st❛ ❞❛ ❣r❛♥✉❧✐ ✭❝❡❧❧❡ ✐rr❡❣♦❧❛r✐ ❞✐ ❝♦♥✈❡③✐♦♥❡✮ ❝♦♥ ✈✐t❛ ♠❡❞✐❛ ❞✐ ♣♦❝❤✐ ♠✐♥✉t✐✱

❞❛ ♣✐❝❝♦❧❡ ❛r❡❡ ❜✉✐❡ ❝❤✐❛♠❛t❡ ♣♦r✐ ❡ ❞❛ ❛r❡❡ ❜✉✐❡ ♣✐ù ❣r❛♥❞✐✿ ❧❡ ♠❛❝❝❤✐❡ s♦❧❛r✐✳ ▲♦ str❛t♦

❡st❡r♥♦ ❞❡❧❧❛ ③♦♥❛ ❝♦♥✈❡tt✐✈❛ è ❞❡tt♦ ❢♦t♦s❢❡r❛✳ ■❧ ♠❛r❣✐♥❡ ❞❡❧❧❛ ❢♦t♦s❢❡r❛ è ♥❡tt❛♠❡♥t❡

❞❡✜♥✐t♦ ❡ r✐s✉❧t❛ s♦st❛♥③✐❛❧♠❡♥t❡ ♦♣❛❝♦ ♣♦✐❝❤è ✐ ❣❛s ❞✐ ❝✉✐ è ❝♦♠♣♦st♦ s♦♥♦ ❢♦rt❡♠❡♥t❡

✐♦♥✐③③❛t✐ ❡ ♣♦ss♦♥♦ ❛ss♦r❜✐r❡ ❡❞ ❡♠❡tt❡r❡ ✉♥♦ s♣❡ttr♦ ❝♦♥t✐♥✉♦ ❞✐ r❛❞✐❛③✐♦♥❡✳ P❡rt❛♥t♦

❧❛ ❢♦t♦s❢❡r❛ è s♦r❣❡♥t❡ ❞❡❧❧❛ ♠❛❣❣✐♦r ♣❛rt❡ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡✳ ❊st❡r♥❛♠❡♥t❡ s✐ tr♦✈❛

✉♥✬❛t♠♦s❢❡r❛ s♦❧❛r❡ ♣✐ù ♦ ♠❡♥♦ tr❛s♣❛r❡♥t❡✱ ♦ss❡r✈❛❜✐❧❡ ❞✉r❛♥t❡ ❧❡ ❡❝❧✐ss✐ ❞✐ t♦t❛❧✐ ❞✐ ❙♦❧❡

♦ ♠❡❞✐❛♥t❡ str✉♠❡♥t✐ ❝❤❡ ♦❝❝✉❧t✐♥♦ ✐❧ ❞✐s❝♦ s♦❧❛r❡✳ ❙♦♣r❛ ❧❛ ❢♦t♦s❢❡r❛ ✈✐ è ✉♥♦ str❛t♦ ❞✐ ❣❛s

♠❡t❛♥♦ ❝❛❧❞♦ ♣r♦❢♦♥❞♦ ❞✐✈❡rs❡ ❝❡♥t✐♥❛✐❛ ❞✐ ❝❤✐❧♦♠❡tr✐ ❞❡tt♦ str❛t♦ ❞✐ ✐♥✈❡rs✐♦♥❡✳ ❊st❡r♥❛✲

♠❡♥t❡ ❛ q✉❡st♦ s✐ tr♦✈❛ ❧❛ ❝r♦♠♦s❢❡r❛✿ s✐ tr❛tt❛ ❞✐ ✉♥♦ str❛t♦ ❣❛ss♦s♦ ❝♦♥ ✉♥❛ t❡♠♣❡rt✉r❛

s✉♣❡r✐♦r❡ ❛ q✉❡❧❧❛ ❞❡❧❧❛ ❢♦t♦s❢❡r❛ ❡ ❞✐ ♠✐♥♦r❡ ❞❡♥s✐tà✳ ❆♥❝♦r❛ ♣✐ù ❡st❡r♥❛♠❡♥t❡ s✐ tr♦✈❛ ❧❛

❝♦r♦♥❛✱ ❞✐ ❞❡♥s✐tà ♠♦❧t♦ ❜❛ss❛ ❡ ❛❞ ✉♥❛ t❡♠♣❡r❛t✉r❛ ♠♦❧t♦ ❛❧t❛ ✭106K✮✳

◗✉❡st❛ ❞❡s❝r✐③✐♦♥❡ s❡♠♣❧✐✜❝❛t❛ ❞❡❧ ❙♦❧❡✱ ❞❡❧❧❛ s✉❛ str✉tt✉r❛ ✜s✐❝❛ ❡ ❞❡✐ s✉♦✐ ❣r❛❞✐❡♥t✐ ❞✐

t❡♠♣❡r❛t✉r❛ s❡r✈❡ ❛ ❝♦♠♣r❡♥❞❡r❡ ❝❤❡ ✐❧ ❙♦❧❡ ♥♦♥ s✐ ❝♦♠♣♦rt❛✱ ✐♥ r❡❛❧tà✱ ❝♦♠❡ ✉♥ ❝♦r♣♦ ♥❡r♦

❛ ✉♥❛ t❡♠♣❡r❛t✉r❛ ❞❡t❡r♠✐♥❛t❛✳ ▲❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ❡♠❡ss❛ è ❛❧ ❝♦♥tr❛r✐♦ ✐❧ ❝♦♠♣❧❡ss♦

✶✺

r✐s✉❧t❛t♦ ❞✐ ♠♦❧t✐ str❛t✐ ❝❤❡ ❡♠❡tt♦♥♦ ❡ ❛ss♦r❜♦♥♦ r❛❞✐❛③✐♦♥❡ ❞✐ ✈❛r✐❛ ❧✉♥❣❤❡③③❛ ❞✬♦♥❞❛✳

❚✉tt❛✈✐❛ ♣❡r ♠♦❧t❡ ❛♣♣❧✐❝❛③✐♦♥✐✱ ❝♦♥s✐❞❡r❛r❡ ✐❧ ❙♦❧❡ ❝♦♠❡ ✉♥ ❝♦r♣♦ ♥❡r♦ ❛ ✉♥❛ t❡♠♣❡r❛t✉r❛

❞✐ ❝✐r❝❛ 6000 K✱ ♣✉ò ❡ss❡r❡ r✐t❡♥✉t❛ ✉♥✬❛♣♣r♦ss✐♠❛③✐♦♥❡ r❛❣✐♦♥❡✈♦❧❡❀ ♣❡r ❛❧tr✐ ♣r♦❝❡ss✐

❞✐♣❡♥❞❡♥t✐ ❞❛❧❧❛ ❧✉♥❣❤❡③③❛ ❞✬♦♥❞❛✱ ♣❡r ✐ q✉❛❧✐ ❧❛ ❞✐str✐❜✉③✐♦♥❡ s♣❡ttr❛❧❡ è ❞❡t❡r♠✐♥❛♥t❡

✭♣r♦❝❡ss✐ ❢♦t♦❝❤✐♠✐❝✐ ❡ ❢♦t♦✈♦❧t❛✐❝✐✮✱ è ♥❡❝❡ss❛r✐♦ ❛♥❛❧✐③③❛r❡ ❧♦ s♣❡ttr♦ ✐♥ ♠❛❣❣✐♦r❡ ❞❡tt❛❣❧✐♦✳

✷✳✹✳✷ ▲❛ ❈♦st❛♥t❡ ❙♦❧❛r❡

■♥ ❋✐❣✉r❛ ✷✳✹ è ♠♦str❛t❛ s❝❤❡♠❛t✐❝❛♠❡♥t❡ ❧❛ ❞✐s♣♦s✐③✐♦♥❡ ❣❡♦♠❡r✐❝❛ r❡❧❛t✐✈❛ ❙♦❧❡✲

❚❡rr❛✿ ❛❧❧❛ ❞✐st❛♥③❛ ❞✐ ✉♥✬✉♥✐tà ❛str♦♥♦♠✐❝❛✱ ♣❛r✐ ❛❧❧❛ ❞✐st❛♥③❛ ♠❡❞✐❛ ❙♦❧❡✲❚❡rr❛ ✭1.495 ·

1011m✮✱ ✐❧ ❙♦❧❡ s♦tt❡♥❞❡ ✉♥ ❛♥❣♦❧♦ ❞✐ 32◦✳

❋✐❣✉r❛ ✷✳✹✿ ❉✐s♣♦s✐③✐♦♥❡ ❣❡♦♠❡tr✐❝❛ r❡❧❛t✐✈❛ ❙♦❧❡✲❚❡rr❛ ✭❞❛✿ ❏♦❤♥ ❆✳ ❉✉✣❡✱ ❲✐❧❧✐❛♠ ❆✳❇❡❝❦♠❛♥✱ ❙♦❧❛r ❊♥❣✐♥❡❡r✐♥❣ ❚❤❡r♠❛❧ Pr♦❝❡ss♦r✱ ❏♦❤♥ ❲✐❧❡② ✫ ❙♦♥s✱ ■♥❝✳✱ ✶✾✽✵✮

▲❛ r❛❞✐❛③✐♦♥❡ ❡♠❡ss❛ ❞❛❧ ❙♦❧❡ ❡ ❧❛ s✉❛ ❞✐s♣♦s✐③✐♦♥❡ r✐s♣❡tt♦ ❛❧❧❛ ❚❡rr❛ ❢❛♥♥♦ sì ❝❤❡ ❧✬✐♥✲

t❡♥s✐tà ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ❛❧ ❞✐ ❢✉♦r✐ ❞❡❧❧❛ ❛t♠♦s❢❡r❛ t❡rr❡str❡ s✐❛ ♣r❡ss♦❝❤è ❝♦st❛♥t❡✳

❚❛❧❡ ❣r❛♥❞❡③③❛ ♣r❡♥❞❡ ✐❧ ♥♦♠❡ ❞✐ ❈♦st❛♥t❡ ❙♦❧❛r❡✱ Gsc✱ ❡❞ è ❞❡✜♥✐t❛ ❝♦♠❡ ❧✬❡♥❡r❣✐❛ ♣r♦✲

✈❡♥✐❡♥t❡ ❞❛❧ ❙♦❧❡ ♥❡❧❧✬✉♥✐tà ❞✐ t❡♠♣♦ ♣❡r ✉♥✐tà ❞✐ ❛r❡❛ ❞✐ ✉♥❛ s✉♣❡r✜❝✐❡ ♣❡r♣❡♥❞✐❝♦❧❛r❡

❛❧❧❛ ❞✐r❡③✐♦♥❡ ❞✐ ♣r♦♣❛❣❛③✐♦♥❡ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡✱ ♣♦st❛ ❛❞ ✉♥❛ ❞✐st❛♥③❛ ❞❛❧ ❙♦❧❡ ♣❛r✐ ❛❧✲

❧❛ ❞✐st❛♥③❛ ♠❡❞✐❛ ❚❡rr❛✲❙♦❧❡ ❛❧ ❞✐ ❢✉♦r✐ ❞❡❧❧✬❛t♠♦s❢❡r❛✳ Pr✐♠❛ ❞❡❧❧✬❛✈✈❡♥t♦ ❞✐ ❧❛❜♦r❛t♦r✐

✶✻

s♣❛③✐❛❧✐✱ ❧❡ ✈❛❧✉t❛③✐♦♥✐ ❞❡❧❧❛ ❈♦st❛♥t❡ ❙♦❧❛r❡ ✈❡♥✐✈❛♥♦ ❡✛❡tt✉❛t❡ s✉❧❧❛ ❜❛s❡ ❞✐ ♠✐s✉r❛③✐♦♥✐

t❡rr❡str✐ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ tr❛s♠❡ss❛ ❛ttr❛✈❡rs♦ ❧✬❛t♠♦s❢❡r❛✱ ♦✈✈❡r♦ ❞♦♣♦ ❛✈❡r s✉❜✐t♦

✉♥ ♣r♦❝❡ss♦ ❞✐ ♣❛r③✐❛❧❡ ❛ss♦r❜✐♠❡♥t♦ ❡ ❞✐✛✉s✐♦♥❡ ❞❛ ♣❛rt❡ ❞❡❧❧✬❛t♠♦s❢❡r❛ st❡ss❛✳ ❙t✉❞✐

♣✐♦♥✐❡r✐st✐❝✐ ✐♥ q✉❡st♦ s❡♥s♦ ❢✉r♦♥♦ ❡s❡❣✉t✐ ❞❛ ❈✳●✳ ❆❜❜♦t ❡ ❝♦❧❧❛❜♦r❛t♦r✐ ❛❧ ❙♠✐t❤s♦♥✐❛♥

■♥st✐t✉t✐♦♥✳ ◗✉❡st✐ st✉❞✐ ❡ s✉ss❡❣✉❡♥t✐ ♠✐s✉r❡ ❡✛❡tt✉❛t❡ ❞❛ ❧❛❜♦r❛t♦r✐ s♣❛③✐❛❧✐ ❢✉r♦♥♦ r✐✲

♣r❡s❡ ❞❛ ❏♦❤♥s♦♥ ✭✶✾✺✹✮✿ ✐❧ ✈❛❧♦r❡ ❞❡❧❧❛ ❝♦st❛♥t❡ s♦❧❛r❡ st✐♠❛t♦ ❞❛ ❆❜❜♦t✱ 1322 W/m2✱

❢✉ r✐❡❧❛❜♦r❛t♦ ❞❛ ❏♦❤♥s♦♥ ❝❤❡ tr♦✈ò 1395 W/m2✳ P✐ù r❡❝❡♥t❡♠❡♥t❡✱ ❛ ♣❛rt✐r❡ ❞❛❣❧✐ ❛♥♥✐

✬✽✵✱ ❧❛ ❞✐s♣♦♥✐❜✐❧✐tà ❞✐ ❧❛❜♦r❛t♦r✐ ❛❞ ❛❧t❛ q✉♦t❛✱ ♣❛❧❧♦♥✐ ❡ ✈❡✐❝♦❧✐ s♣❛③✐❛❧✐✱ ❤❛ ❝♦♥s❡♥t✐t♦ ❞✐

❡s❡❣✉✐r❡ ♠✐s✉r❡ ❞✐r❡tt❡ ❞❡❧❧✬✐♥t❡♥s✐tà s♦❧❛r❡ ❛❧ ❞✐ ❢✉♦r✐ ❞❡❧❧✬❛t♠♦s❢❡r❛ t❡rr❡str❡✳

■♥ q✉❡st❛ ✐♥❞❛❣✐♥❡ s✐ ❛❞♦tt❛ ✐❧ ✈❛❧♦r❡ ❞❡❧❧❛ ❈♦st❛♥t❡ ❙♦❧❛r❡ Gsc ✜ss❛t♦ ❞❛❧ ❲♦r❧❞ ❘❛❞✐❛t✐♦♥

❈❡♥t❡r ✭❲❘❈✮ ♣❛r✐ ❛ 1367 W/m2 ❝♦♥ ✉♥ ❡rr♦r❡ ❞❡❧❧✬♦r❞✐♥❡ ❞❡❧❧✬1%✳

✷✳✹✳✸ ❈❛❧❝♦❧✐ s✉❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡

❉❡✜♥✐③✐♦♥✐

❘❛❞✐❛③✐♦♥❡ ❞✐r❡tt❛✿ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ♣r♦✈❡♥✐❡♥t❡ ❞❛❧ ❙♦❧❡ s❡♥③❛ ❝❤❡ s✉❜✐s❝❛ ❛❧❝✉♥❛ ❞❡✈✐❛✲

③✐♦♥❡ ❞❛ ♣❛rt❡ ❞❡❧❧✬❛t♠♦s❢❡r❛✳

❘❛❞✐❛③✐♦♥❡ ❞✐✛✉s❛✿ r❛❞✐❛③✐♦♥❡ ♣r♦✈❡♥✐❡♥t❡ ❞❛❧ ❙♦❧❡ ❝❤❡ ❤❛ s✉❜✐t♦ ✉♥ ♣r♦❝❡ss♦ ❞✐ r✐✢❡ss✐♦♥❡

♦ ❞✐✛✉s✐♦♥❡ ❞❛ ♣❛rt❡ ❞❡❧❧❛ ❛t♠♦s❢❡r❛✳

❘❛❞✐❛③✐♦♥❡ t♦t❛❧❡✿ s♦♠♠❛ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ ❞✐r❡tt❛ ❡ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ ❞✐✛✉s❛✱ ❝♦♠✉♥❡♠❡♥t❡

♦❣❣❡tt♦ ❞✐ ♠✐s✉r❛③✐♦♥❡ str✉♠❡♥t❛❧❡✳

❚❡♠♣♦ s♦❧❛r❡ ❡❞ ❡q✉❛③✐♦♥❡ ❞❡❧ t❡♠♣♦✿ ✐❧ t❡♠♣♦ ❝❤❡ ❝♦♠♣❛r❡ ✐♥ t✉tt❡ ❧❡ r❡❧❛③✐♦♥✐ ❣❡♦♠❡tr✐✲

❝❤❡ r❡❧❛t✐✈❡ ❛❧❧❛ ♣♦s✐③✐♦♥❡ ❞❡❧ ❙♦❧❡ è ✐❧ t❡♠♣♦ s♦❧❛r❡✱ ❝❤❡ ♥♦♥ ❝♦✐♥❝✐❞❡ ❝♦♥ ❧✬♦r❛ ❧♦❝❛❧❡✳ ❊✬

♥❡❝❡ss❛r✐♦ ♣❡rt❛♥t♦ ❝♦♥✈❡rt✐r❡ ✐❧ t❡♠♣♦ ❝♦♥✈❡♥③✐♦♥❛❧❡ ♥❡❧ t❡♠♣♦ s♦❧❛r❡✱ ✐❧ ❝❤❡ ❝♦♠♣♦rt❛ ❞✉❡

t✐♣✐ ❞✐ ❝♦rr❡③✐♦♥✐✳ ■♥ ♣r✐♠♦ ❧✉♦❣♦ ❝✬è ✉♥❛ ❝♦rr❡❧❛③✐♦♥❡ ❝♦st❛♥t❡ ♣❡r ❧✬❡✈❡♥t✉❛❧❡ ❞✐✛❡r❡♥③❛

❢r❛ ❧♦♥❣✐t✉❞✐♥❡ ❞❡❧❧❛ ❧♦❝❛❧✐tà ✐♥ q✉❡st✐♦♥❡ ❡❞ ✐❧ ♠❡r✐❞✐❛♥♦ ❞❡❧❧❛ st❛③✐♦♥❡ s✉ ❝✉✐ è ❜❛s❛t❛ ❧✬♦✲

✶✼

r❛ ❝♦♥✈❡③✐♦♥❛❧❡✶✳ ▲❛ s❡❝♦♥❞❛ ❝♦rr❡❧❛③✐♦♥❡ ❞❡r✐✈❛ ❞❛❧❧✬❡q✉❛③✐♦♥❡ ❞❡❧ t❡♠♣♦ ❝❤❡ t✐❡♥❡ ❝♦♥t♦

❞❡❧❧❡ ✈❛r✐❡ ♣❡rt✉r❜❛③✐♦♥✐ ♥❡❧❧✬♦r❜✐t❛ ❞❡❧❧❛ ❚❡rr❛ ❡ ♥❡❧❧❛ ✈❡❧♦❝✐tà ❞✐ r♦t❛③✐♦♥❡ ❝❤❡ s✐ r✐✢❡tt♦✲

♥♦ ✐♥ ✈❛r✐❛③✐♦♥✐ ❞❡❧ t❡♠♣♦ ✐♥ ❝✉✐ ✐❧ ❙♦❧❡ ❛♣♣❛r❡ ❛ttr❛✈❡rs❛r❡ ✐❧ ♠❡r✐❞✐❛♥♦ ❞❡❧❧✬♦ss❡r✈❛t♦r❡✳

▲✬♦r❛ s♦❧❛r❡ ♣✉ò ❡ss❡r❡ r✐❝❛✈❛t❛ ❞❛❧❧✬♦r❛ ❝♦♥✈❡♥③✐♦♥❛❧❡ ♠❡❞✐❛♥t❡ ❧❛ r❡❧❛③✐♦♥❡✿

ora−solare = ora−convenzionale+ E + 4(LSt − LLoc) ✭✷✳✶✶✮

❞♦✈❡ E è ❧✬❡q✉❛③✐♦♥❡ ❞❡❧ t❡♠♣♦ ✭✷✳✶✷✮ ✐♥ ♠✐♥✉t✐✱ LSt è ✐❧ ♠❡r✐❞✐❛♥♦ s✉ ❝✉✐ è ❜❛s❛t❛ ❧✬♦r❛

st❛♥❞❛r❞ ❝♦♥✈❡♥③✐♦♥❛❧❡ ❡ LLoc è ❧❛ ❧♦♥❣✐t✉❞✐♥❡ ❞❡❧❧❛ ❧♦❝❛❧✐tà ❝♦♥s✐❞❡r❛t❛ ❡s♣r❡ss❛ ✐♥ ❣r❛❞✐

♦✈❡st✳

E = 229.2(0.000075 + 0.001868 cosB − 0.032077 sinB

− 0.014615 cos 2B − 0.04089 sin 2B) ✭✷✳✶✷✮

❞♦✈❡✿

B = (n− 1)360

365✭✷✳✶✸✮

❡ n r❛♣♣r❡s❡♥t❛ ✐❧ ♥✉♠❡r♦ ❞❡❧ ❣✐♦r♥♦ ❞❡❧❧✬❛♥♥♦✱ 1 ≤ n ≤ 365✳

❉✐r❡③✐♦♥❡ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ ❞✐r❡tt❛

▲❛ r❡❧❛③✐♦♥❡ ❣❡♦♠❡tr✐❝❛ tr❛ ✉♥ ♣✐❛♥♦ ❝♦♠✉♥q✉❡ ♦r✐❡♥t❛t♦ r✐s♣❡tt♦ ❛❧❧❛ ❚❡rr❛ ❡ ❧❛ ❞✐r❡③✐♦♥❡

❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ❞✐r❡tt❛ ✐♥❝✐❞❡♥t❡✱ ❝✐♦è ❧❛ ♣♦s✐③✐♦♥❡ ❞❡❧ ❙♦❧❡ r✐s♣❡tt♦ ❛❧ ♣✐❛♥♦✱ ♣✉ò

❡ss❡r❡ ❞❡s❝r✐tt❛ ✐♥ ❢✉♥③✐♦♥❡ ❞❡❧ t❡♠♣♦ ♠❡❞✐❛♥t❡ r❡❧❛③✐♦♥✐ tr✐❣♦♥♦♠❡tr✐❝❤❡ ✐♥ ❝✉✐ ❝♦♠♣❛✐♦♥♦

❞✐✈❡rs✐ ❛♥❣♦❧✐✳ ◗✉❡st✐ ❛♥❣♦❧✐ ❡ ❧❡ r❡❧❛③✐♦♥✐ ❝❤❡ ❧✐ ❧❡❣❛♥♦ ✭❇❡♥❢♦r❞ ❡ ❇♦❝❦ ✶✾✸✾✮ s♦♥♦ ❞❡✜♥✐t✐

❡ r✐♣♦rt❛t❡ ♥❡❧ s❡❣✉✐t♦ ✭❋✐❣✉r❛ ✷✳✺✮✳

φ ❂ ❧❛t✐t✉❞✐♥❡✱ ♣♦s✐t✐✈❛ s❡ ❛ ♥♦r❞❀

δ ❂ ❞❡❝❧✐♥❛③✐♦♥❡✿ ♣♦s✐③✐♦♥❡ ❛♥❣♦❧❛r❡ ❞❡❧ ❙♦❧❡ r✐s♣❡tt♦ ❛❧ ♣✐❛♥♦ ❞❡❧❧✬❡q✉❛t♦r❡ ❛ ♠❡③③♦❣✐♦r♥♦✱♣♦s✐t✐✈❛ ✈❡rs♦ ♥♦r❞❀

β ❂ ❛♥❣♦❧♦ ❝♦♠♣r❡s♦ tr❛ ✐❧ ♣✐❛♥♦ ♦r✐③③♦♥t❛❧❡ ❡❞ ✐❧ ♣✐❛♥♦ ❝♦♥s✐❞❡r❛t♦ ✭✐♥❝❧✐♥❛③✐♦♥❡ ❞❡❧❧❛s✉♣❡r✜❝✐❡✮❀

✶P❡r ❧✬■t❛❧✐❛✱ ✐❧ ♠❡r✐❞✐❛♥♦ ❞✐ r✐❢❡r✐♠❡♥t♦ è ✐❧ ♠❡r✐❞✐❛♥♦ 15◦ ❡st r✐s♣❡tt♦ ❛ q✉❡❧❧♦ ❞✐ ●r❡❡♥✇✐t❝❤✳

✶✽

γ ❂ ❛♥❣♦❧♦ ❛③✐♠✉t❛❧❡ ❞❡❧❧❛ s✉♣❡r✜❝✐❡✱ ❝✐♦è ❞❡✈✐❛③✐♦♥❡ ❞❡❧❧❛ ♥♦r♠❛❧❡ ❛❧❧❛ s✉♣❡r✜❝✐❡ ❞❛❧♠❡r✐❞✐❛♥♦ ❧♦❝❛❧❡✱ ③❡r♦ ❛ s✉❞✱ ♣♦s✐t✐✈♦ ✈❡rs♦ ❡st✱ ♥❡❣❛t✐✈♦ ✈❡rs♦ ♦✈❡st❀

ω ❂ ❛♥❣♦❧♦ ♦r❛r✐♦✱ ♣r❡s♦ ③❡r♦ ❛ ♠❡③③♦❣✐♦r♥♦ s♦❧❛r❡✱ ❡ ♣❛r✐ ❛ 15◦ ♣❡r ♦❣♥✐ ♦r❛✱ ♣♦s✐t✐✈♦ ❧❛♠❛tt✐♥❛ ❡ ♥❡❣❛t✐✈♦ ♥❡❧ ♣♦♠❡r✐❣❣✐♦ ✭❛❞ ❡s❡♠♣✐♦✱ ω ❂ +15◦ ❛❧❧❡ ✶✶✳✵✵❀ ω ❂ −37.5◦

❛❧❧❡ ✶✹✳✸✵✮❀

θ ❂ ❛♥❣♦❧♦ ❞✐ ✐♥❝✐❞❡♥③❛ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ ❞✐r❡tt❛✱ ♠✐s✉r❛t♦ ❢r❛ ❧❛ ❞✐r❡③✐♦♥❡ ❞✐ ♣r♦♣❛❣❛③✐♦♥❡❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ ❡ ❧❛ ♥♦r♠❛❧❡ ❛❧❧❛ s✉♣❡r✜❝✐❡❀

θz ❂ ❛♥❣♦❧♦ ③❡♥✐t❛❧❡✱ ❝✐♦è ❧✬❛♥❣♦❧♦ ❝❤❡ ❧❛ r❛❞✐❛③✐♦♥❡ ❞✐r❡tt❛ ❢♦r♠❛ ❝♦♥ ❧❛ ✈❡rt✐❝❛❧❡❀

αs ❂ ❛❧t✐t✉❞✐♥❡ s♦❧❛r❡✱ ❝✐♦è ❧✬❛♥❣♦❧♦ ❝❤❡ ❧❛ r❛❞✐❛③✐♦♥❡ ❞✐r❡tt❛ ❢♦r♠❛ ❝♦♥ ❧✬♦r✐③③♦♥t❛❧❡ ✭♣❛r✐❛ 90◦ − θz✮❀

γs❂ s❝♦st❛♠❡♥t♦ ❛♥❣♦❧❛r❡ ❞❛ s✉❞ ❞❡❧❧❛ ♣r♦✐❡③✐♦♥❡ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ ❞✐r❡tt❛ s✉❧ ♣✐❛♥♦ ♦r✐③✲③♦♥t❛❧❡✳

✭❛✮ ✭❜✮

❋✐❣✉r❛ ✷✳✺✿ ✭❛✮ ❆♥❣♦❧♦ ③❡♥✐t❛❧❡✱ ✐♥❝❧✐♥❛③✐♦♥❡✱ ❛♥❣♦❧♦ ❛③✐♠✉t❛❧❡ ❞❡❧❧❛ s✉♣❡r✜❝✐❡ ❡ s❝♦st❛✲♠❡♥t♦ ❛♥❣♦❧❛r❡ ❞❛ s✉❞ ♣❡r ✉♥❛ s✉♣❡r✜❝✐❡ ✐♥❝❧✐♥❛t❛✳ ✭❜✮ ❙❝♦st❛♠❡♥t♦ ❛♥❣♦❧❛r❡ ❞❛ s✉❞ ❞❡❧❧❛♣r♦✐❡③✐♦♥❡ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ ❞✐r❡tt❛ s✉❧ ♣✐❛♥♦ ♦r✐③③♦♥t❛❧❡✳ ✭❉❛✿ ❏♦❤♥ ❆✳ ❉✉✣❡✱ ❲✐❧❧✐❛♠ ❆✳❇❡❝❦♠❛♥✱ ❙♦❧❛r ❊♥❣✐♥❡❡r✐♥❣ ❚❤❡r♠❛❧ Pr♦❝❡ss♦r✱ ❏♦❤♥ ❲✐❧❡② ✫ ❙♦♥s✱ ■♥❝✳✱ ✶✾✽✵✮✳

▲❛ ❞❡❝❧✐♥❛③✐♦♥❡✱ δ✱ ♣✉ò ❡ss❡r❡ r✐❝❛✈❛t❛ ♠❡❞✐❛♥t❡ ❧❛ r❡❧❛③✐♦♥❡ ❛♣♣r♦ss✐♠❛t❛ ❞✐ ❈♦♦♣❡r

✭✶✾✻✾✮✿

δ = 23.45 sin

[

360 ·284 + n

365

]

✭✷✳✶✹✮

❞♦✈❡ n è ✐❧ ❣✐♦r♥♦ ❞❡❧❧✬❛♥♥♦✳

✶✾

▲❛ r❡❧❛③✐♦♥❡ ❢r❛ θ ❡ ❣❧✐ ❛❧tr✐ ❛♥❣♦❧✐ è ❞❛t❛ ❞❛✿

cos θ = sin δ sinφ cos β − sin δ cosφ sin β cos γ + cos δ cosφ cos β cosω

+ cos δ sinφ sin β cos γ cosω + cos δ sin β sin γ sinω ✭✷✳✶✺✮

♦✈✈❡r♦✱

cos θ = cos θz cos β + sin θz sin β cos(γs − γ) ✭✷✳✶✻✮

P❡r ✐❧ ❝❛❧❝♦❧♦ ❞❡❧❧✬❛♥❣♦❧♦ ③❡♥✐t❛❧❡✱ θz✱ s✐ ✐♠♣✐❡❣❛ ❧❛ r❡❧❛③✐♦♥❡✿

cos θz = cosφ cos δ cosω + sinφ sin δ ✭✷✳✶✼✮

❘❛❞✐❛③✐♦♥❡ ❡①tr❛t❡rr❡str❡ s✉ s✉♣❡r✐✜❝✐❡ ♦r✐③③♦♥t❛❧❡

❊✬ ♣♦ss✐❜✐❧❡ st✐♠❛r❡ ❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ✐♥❝✐❞❡♥t❡ s✉ ✉♥ ♣✐❛♥♦ ♦r✐③③♦♥t❛❧❡ ❛❧ ❞✐ ❢✉♦r✐

❞❡❧❧✬❛t♠♦s❢❡r❛ ❛♣♣❧✐❝❛♥❞♦ ❧✬❡q✉❛③✐♦♥❡✿

I0,extra = Gsc(1 + 0.033 cos360n

365) cos θz ✭✷✳✶✽✮

❞♦✈❡ Gsc è ❧❛ ❈♦st❛♥t❡ ❙♦❧❛r❡ ❡ n è ✐❧ ❣✐♦r♥♦ ❞❡❧❧✬❛♥♥♦✳

❙✐ ❞❡✜♥✐s❝❡ q✉✐♥❞✐ ❧✬✐♥❞✐❝❡ ❞✐ tr❛s♣❛r❡♥③❛ ❞❡❧❧✬❛t♠♦s❢❡r❛ kt✿

kt =I0

I0,extra✭✷✳✶✾✮

❞♦✈❡ I0 è ❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ t♦t❛❧❡ s✉ s✉♣❡r✜❝✐❡ ♦r✐③③♦♥t❛❧❡ ♦tt❡♥✉t❛ ❞❛ ♠✐s✉r❛③✐♦♥✐

str✉♠❡♥t❛❧✐✳

❙✉❞❞✐✈✐s✐♦♥❡ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ ✐♥ ❞✐r❡tt❛ ❡❞ ✐♥ ❞✐✛✉s❛

■♥ ❧❡tt❡r❛t✉r❛ s♦♥♦ ❞✐s♣♦♥✐❜✐❧✐ ❞✐✈❡rs✐ ♠❡t♦❞✐✱ r✐❝❛✈❛t✐ s✉ ❜❛s❡ s♣❡r✐♠❡♥t❛❧❡✱ ♣❡r st✐♠❛r❡

❧❛ ❞✐str✐❜✉③✐♦♥❡ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ✐♥ ❞✐r❡tt❛ ❡❞ ✐♥ ❞✐✛✉s❛ ❛ ♣❛rt✐r❡ ❞❛❧❧❛ r❛❞✐❛③✐♦♥❡

t♦t❛❧❡ ✐♥❝✐❞❡♥t❡ s✉ ♣✐❛♥♦ ♦r✐③③♦♥t❛❧❡✳ ❚✉tt✐ ✐ ♠❡t♦❞✐ ♣r♦♣♦st✐ ❝♦rr❡❧❛♥♦ ✐❧ r❛♣♣♦rt♦ tr❛

r❛❞✐❛③✐♦♥❡ ❞✐✛✉s❛ ❡ r❛❞✐❛③✐♦♥❡ t♦t❛❧❡ s✉ ♣✐❛♥♦ ♦r✐③③♦♥t❛❧❡ I0,d/I✱ ❝♦♥ ❧✬✐♥❞✐❝❡ ❞✐ tr❛s♣❛r❡♥③❛

❞❡❧❧✬❛t♠♦s❢❡r❛ kt✳

✷✵

❋✐❣✉r❛ ✷✳✻✿ ❊s❡♠♣✐♦ ❞❡❧ r❛♣♣♦rt♦ I0,d/I ✐♥ ❢✉♥③✐♦♥❡ ❞✐ kt ✭❞❛ ❘❡✐♥❞❧ ✭✶✾✽✽✮✮

■♥ ❋✐❣✉r❛ ✷✳✻ è r✐♣♦rt❛t♦ ✉♥ ❡s❡♠♣✐♦ ❞✐ ❞❛t✐ ♠✐s✉r❛t✐ ❛ ❈❛♣❡ ❈❛♥❛✈❡r❛❧✱ ❋▲ ❙t❛t✐ ❯♥✐t✐✱

♠❡♥tr❡ ✐♥ ❋✐❣✉r❛ ✷✳✼ s✐ ❝♦♥❢r♦♥t❛♥♦ ❣❧✐ ❛♥❞❛♠❡♥t✐ ❞❡❧❧❡ r❡❧❛③✐♦♥✐ ❛♥❛❧✐t✐❝❤❡ ♦tt❡♥✉t❡ ❞❛

❞✐✈❡rs✐ ❆✉t♦r✐ ❝❤❡ ❤❛♥♥♦ ✉s❛t♦ ❞❛t✐ ❞✐ ♣❛rt❡♥③❛ ♣r♦✈❡♥✐❡♥t✐ ❞❛ st❛③✐♦♥✐ ✐♥ ♣✉♥t✐ ❞✐✈❡rs✐ ❞❡❧

▼♦♥❞♦✳

❋✐❣✉r❛ ✷✳✼✿ ❆♥❞❛♠❡♥t✐ ❞✐ I0,d/I ✐♥ ❢✉♥③✐♦♥❡ ❞✐ kt ♦tt❡♥✉t✐ ❞❛ ❖r❣✐❧❧ ❡ ❍♦❧❧❛♥❞s ✭✶✾✼✼✮✱❊r❜s ❡t ❛❧✳ ✭✶✾✽✷✮ ❡ ❘❡✐♥❞❧ ❡t ❛❧✳ ✭✶✾✾✵✮

❙✐ ♦ss❡r✈❛ ✉♥ s♦st❛♥③✐❛❧❡ ❛❝❝♦r❞♦ ❞❡✐ r✐s✉❧t❛t✐ ♦tt❡♥✉t✐✱ s❡❜❜❡♥❡ ❖r❣✐❧❧ ❡ ❍♦❧❧❛♥❞s ✭✶✾✼✼✮

❛❜❜✐❛♥♦ ✐♠♣✐❡❣❛t♦ ❞❛t✐ ♣r♦✈❡♥✐❡♥t✐ ❞❛ st❛③✐♦♥✐ ✐♥ ❈❛♥❛❞❛✱ ❊r❜s ❡t ❛❧✳ ✭✶✾✽✷✮ ❞❛ st❛③✐♦♥✐

♥❡❣❧✐ ❙t❛t✐ ❯♥✐t✐ ❡❞ ❆✉str❛❧✐❛ ❡ ❘❡✐♥❞❧ ❡t ❛❧✳ ✭✶✾✾✵✮ ❞❛ st❛③✐♦♥✐ ✐♥ ❊✉r♦♣❛ ❡ ❙t❛t✐ ❯♥✐t✐✳

✷✶

P❡r ❧❡ ✈❛❧✉t❛③✐♦♥✐ ❞✐ q✉❡st❛ ✐♥❞❛❣✐♥❡ s✐ s♦♥♦ ✉t✐❧✐③③❛t❡ ❧❡ ❝♦rr❡❧❛③✐♦♥✐ ♣r♦♣♦st❡ ❞❛ ❊r❜s ❡t

❛❧✳✿

I0,dI0

=

1.0− 0.09kt ♣❡r kt ≤ 0.22

0.9511− 0.1604kt + 4.388k2

t ♣❡r 0.22 < kt ≤ 0.80

0.165 ♣❡r kt > 0.80

✭✷✳✷✵✮

❘❛♣♣♦rt♦ tr❛ r❛❞✐❛③✐♦♥❡ s✉ s✉♣❡r✜❝✐❡ ✐♥❝❧✐♥❛t❛ ❡ s✉ s✉♣❡r✜❝✐❡ ♦r✐③③♦♥t❛❧❡

❉❛❧❧❡ ♠✐s✉r❛③✐♦♥✐ ❞✐r❡tt❡ ❡ ❞❛❧❧✬❛♣♣❧✐❝❛③✐♦♥❡ ❞❡✐ ♠❡t♦❞✐ ❡s♣♦st✐ s✐ r✐❝❛✈❛♥♦ ❧❛ r❛❞✐❛③✐♦♥❡

s♦❧❛r❡ ❞✐r❡tt❛ ❡ ❞✐✛✉s❛ s✉❧ ♣✐❛♥♦ ♦r✐③③♦♥t❛❧❡✱ t✉tt❛✈✐❛✱ ♣❡r ❣❧✐ s❝♦♣✐ ❞✐ q✉❡st✬✐♥❞❛❣✐♥❡✱

♦❝❝♦rr❡ ❝♦♥♦s❝❡r♥❡ ✐ ✈❛❧♦r✐ s✉❧❧❛ s✉♣❡r✜❝✐❡ ✐♥❝❧✐♥❛t❛ ❞❡❧❧✬❛♥❣♦❧♦ β r✐s♣❡tt♦ ❧✬♦r✐③③♦♥t❛❧❡✳

❙♦♥♦ ❞✐s♣♦♥✐❜✐❧✐ r❡❧❛③✐♦♥✐ ♣✉r❛♠❡♥t❡ ❣❡♦♠❡tr✐❝❤❡ ❝❤❡ ♣❡r♠❡tt♦♥♦ ❞✐ ❝❛❧❝♦❧❛r❡ ✐❧ r❛♣♣♦rt♦

tr❛ r❛❞✐❛③✐♦♥❡ ❞✐r❡tt❛ s✉ s✉♣❡r✜❝✐❡ ✐♥❝❧✐♥❛t❛ IT,b ❡ s✉ s✉♣❡r✜❝✐❡ ♦r✐③③♦♥t❛❧❡ I0,b✿

Rb =IT,bI0,b

=cos θ

cos θz✭✷✳✷✶✮

✐❧ r❛♣♣♦rt♦ tr❛ r❛❞✐❛③✐♦♥❡ ❞✐✛✉s❛ s✉ s✉♣❡r✜❝✐❡ ✐♥❝❧✐♥❛t❛ IT,d ❡ s✉ s✉♣❡r✜❝✐❡ ♦r✐③③♦♥t❛❧❡ I0,d✿

Rd =IT,dI0,d

=1 + cos β

2✭✷✳✷✷✮

❡❞ ✐❧ r❛♣♣♦rt♦ tr❛ r❛❞✐❛③✐♦♥❡ r✐✢❡ss❛ ❞❛❧❧✬❛♠❜✐❡♥t❡ ❝✐r❝♦st❛♥t❡ s✉❧❧❛ s✉♣❡r✜❝✐❡ ✐♥❝❧✐♥❛t❛ IT,r

❡ ❧❛ r❛❞✐❛③✐♦♥❡ t♦t❛❧❡ s✉ s✉♣❡r✜❝✐❡ ♦r✐③③♦♥t❛❧❡ I0✿

Rr =IT,rI0

= ρg(1− cos β

2) ✭✷✳✷✸✮

❞♦✈❡ ρg è ❧✬❛❧❜❡❞♦ ❞❡❧❧❡ s✉♣❡r✜❝✐ ❞❡❧❧✬❛♠❜✐❡♥t❡ ❝✐r❝♦st❛♥t❡✳

◗✉✐♥❞✐ ❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ t♦t❛❧❡ ✐♥❝✐❞❡♥t❡ s✉ ✉♥❛ ❣❡♥❡r✐❝❛ s✉♣❡r✜❝✐❡ ✐♥❝❧✐♥❛t❛ ❞✐ ✉♥ ❛♥❣♦❧♦

β r✐s♣❡tt♦ ❧✬♦r✐③③♦♥t❛❧❡ r✐s✉❧t❛ s♦♠♠❛ ❞✐ tr❡ t❡r♠✐♥✐✿

IT = IT,b + IT,d = I0,bRb + I0,dRd + I0Rr ✭✷✳✷✹✮

✷✷

❆♣♣❧✐❝❛③✐♦♥❡ ❛❧ ❝❛s♦ ❞✐ st✉❞✐♦

▲✬❛♣♣❧✐❝❛③✐♦♥❡ ❞❡❧❧❡ ❡q✉❛③✐♦♥✐ ♣r❡s❡♥t❛t❡ ♥❡❧ P❛r❛❣r❛❢♦ ✷✳✹✳✸ r✐❝❤✐❡❞❡ ❝❤❡ s✐❛♥♦ ❞❡✜♥✐t❡

❧❡ ✈❛r✐❛❜✐❧✐ r❡❧❛t✐✈❡ ❛❧ ❣✐♦r♥♦ ❡❞ ❛❧ ❧✉♦❣♦ ❞✐ st✉❞✐♦ ❡ ❧✬✐♥t❡r✈❛❧❧♦ t❡♠♣♦r❛❧❡ ✐♥t❡r❡ss❛t♦✳ ■♥

♣❛rt✐❝♦❧❛r❡ ✐♥ ❚❛❜❡❧❧❛ ✷✳✶ s♦♥♦ r✐♣♦rt❛t✐ ✐ ❞❛t✐ ✐♥ ✐♥❣r❡ss♦ ♣❡r ✐❧ ❣✐♦r♥♦ ✸✵ ❧✉❣❧✐♦ ✐♥ P✳③③❛

●❤✐❛✐❛ ❛ P❛r♠❛ ✭❋✐❣✉r❛ ✷✳✽ ✮✳ ▲❛ ♣r♦❝❡❞✉r❛ ❞✐ ❝❛❧❝♦❧♦ ❢♦r♥✐s❝❡ ✐♥ ✉s❝✐t❛✱ ✐♥ ❢✉♥③✐♦♥❡ ❞❡❧

t❡♠♣♦✱ ✐ ✈❛❧♦r✐ ❛ss✉♥t✐ ❞❛❧❧✬❛♥❣♦❧♦ ❞✐ ✐♥❝✐❞❡♥③❛ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ❞✐r❡tt❛✱ θ✱ ❡❞ ✐ ✈❛❧♦r✐

❞❡❧❧✬✐♥t❡♥s✐tà ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ❞✐r❡tt❛✱ IT,b✱ ❡ ❞✐✛✉s❛✱ IT,d✱ s✉❧❧❛ ❝♦♣❡rt✉r❛ ✐♥ ✈❡tr♦✳

❋✐❣✉r❛ ✷✳✽✿ ❈♦♣❡rt✉r❛ ✐♥ ✈❡tr♦✱ P✳③③❛ ●❤✐❛✐❛✱ P❛r♠❛

▲❛t✐t✉❞✐♥❡ φ 44.80◦

▲♦♥❣✐t✉❞✐♥❡ 10.32◦

P❡♥❞❡♥③❛ ❝♦♣❡rt✉r❛ β 5◦

❆♥❣♦❧♦ ❛③✐♠✉t❛❧❡ γ −66◦

●✐♦r♥♦ ❞❡❧❧✬❛♥♥♦ n 211

❈♦st❛♥t❡ s♦❧❛r❡ Gsc 1367 W/m2

❆❧❜❡❞♦ ❞❡❧❧❡ s✉♣❡r✜❝✐ ❝✐r❝♦st❛♥t✐ ρg 0.20

▼❡r✐❞✐❛♥♦ ❞✐ r✐❢❡r✐♠❡♥t♦ LSt +15◦

■♥t❡r✈❛❧❧♦ t❡♠♣♦r❛❧❡ 11 : 00÷ 14 : 45

P❛ss♦ 10 s

❚❛❜❡❧❧❛ ✷✳✶✿ ❊s❡♠♣✐♦ ❞❛t✐ ✐♥ ✐♥❣r❡ss♦ ♣❡r ✐❧ ❣✐♦r♥♦ ✸✵ ▲✉❣❧✐♦ ✷✵✶✷✱ P✳③③❛ ●❤✐❛✐❛ P❛r♠❛

✷✸

✷✳✺ Pr♦♣r✐❡tà ❞❡❧❧❛ ❝♦♣❡rt✉r❛ ✐♥ ✈❡tr♦

■ ❞❛t✐ ❢♦r♥✐t✐ ❞❛❧ ❝♦str✉tt♦r❡ ❞❡❧ s✐♥❣♦❧♦ ♣❛♥♥❡❧❧♦ ❞✐ ✈❡tr♦ ♥♦♥ s♦♥♦ s✉✣❝✐❡♥t✐ ❡ ♥♦♥

♣❡r♠❡tt♦♥♦ ❞✐ ❞❡s❝r✐✈❡r❡ ✐♥ ♠❛♥✐❡r❛ ❡s❛✉st✐✈❛ ❧❡ ♣r♦♣r✐❡tà ❡♥❡r❣❡t✐❝❤❡ ❞❡❧❧✬✐♥t❡r❛ ❝♦♣❡rt✉✲

r❛✳ ■♥❢❛tt✐✱ ♦❧tr❡ ❛❧ ❢❛tt♦ ❝❤❡ s♦♥♦ ❞✐❝❤✐❛r❛t❡ ❧❡ s♦❧❡ ❝❛r❛tt❡r✐st✐❝❤❡ ❡♥❡r❣❡t✐❝❤❡ ❡♠✐s❢❡r✐❝❤❡

❞❡❧ ✈❡tr♦✱ ♠❡♥tr❡ ❧❛ ♣r♦❝❡❞✉r❛ ❞✐ ❝❛❧❝♦❧♦ r✐❝❤✐❡❞❡ ✉♥❛ ❝❛r❛tt❡r✐③③❛③✐♦♥❡ ✐♥ ❢✉♥③✐♦♥❡ ❞❡❧✲

❧✬❛♥❣♦❧♦ ❞✐ ✐♥❝✐❞❡♥③❛ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡✱ ♦✈✈❡r♦ ✐♥ ❢✉♥③✐♦♥❡ ❞❡❧ t❡♠♣♦✱ ♦❝❝♦rr❡ t❡♥❡r

❝♦♥t♦ ❛♥❝❤❡ ❞✐ ❛❧tr✐ ❢❛tt♦r✐ ❝❤❡ ❤❛♥♥♦ ♥♦t❡✈♦❧❡ ✐♥✢✉❡♥③❛ q✉❛❧✐✿ ❧❛ ♣r❡s❡♥③❛ ❞✐ s❡r✐❣r❛✜❡

❝♦♥ ❞✐✈❡rs✐ ❣r❛❞✐ ❞✐ ❛ss♦r❜✐♠❡♥t♦ ❞✐s♣♦st❡ s✉✐ ♣❛♥♥❡❧❧✐ ✭❚❛❜❡❧❧❛ ✶✳✷ ✮✱ ❧✬❡✛❡tt♦ ❞❡❧❧❛ ♣♦❧✈❡r❡

♣r❡s❡♥t❡ s✉❧❧❛ ❝♦♣❡rt✉r❛ ✭❆❞❡❧ ❆✳ ❍❡❣❛③② ❬✽❪✮✱ ❧✬❡✛❡tt♦ ❞❡❧❧❛ str✉tt✉r❛ ♣♦rt❛♥t❡ ♠❡t❛❧❧✐❝❛

❡ ❧❛ ♣r❡s❡♥③❛ ❞❡❧❧❡ ❛♣❡rt✉r❡ ❧❛t❡r❛❧✐ ✭❋✐❣✉r❛ ✷✳✾✮✳ ❙✐ è ♣❡rt❛♥t♦ ♣r♦❝❡❞✉t♦ ❝♦♥ ✉♥❛ ❝❛✲

r❛tt❡r✐③③❛③✐♦♥❡ s♣❡r✐♠❡♥t❛❧❡ ✐♥ ❧♦❝♦ ❞❡❧❧✬✐♥t❡r♥❛ ❝♦♣❡rt✉r❛ ♣❡r ♦tt❡♥❡r❡ ✐ ✈❛❧♦r✐ ❡✛❡tt✐✈✐ ❞✐

❛ss♦r❜✐♠❡♥t♦✱ tr❛s♠✐ss✐♦♥❡ ❡ r✐✢❡ss✐♦♥❡ ❡♠✐s❢❡r✐❝✐ ❡❞ ✐♥ ❢✉♥③✐♦♥❡ ❞❡❧❧✬❛♥❣♦❧♦ ❞✐ ✐♥❝✐❞❡♥③❛

❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ❞✐r❡tt❛✳

❋✐❣✉r❛ ✷✳✾✿ ❈♦♣❡rt✉r❛ ✐♥ ♣❛♥♥❡❧❧✐ ❞✐ ✈❡tr♦ s❡r✐❣r❛❢❛t♦ ❡ str✉tt✉r❛ ♠❡t❛❧❧✐❝❛

❉✐s♣♦♥❡♥❞♦ ❞✉❡ s♦❧❛r✐♠❡tr✐ ❝♦♠❡ ♠♦str❛t♦ ♥❡❧❧♦ s❝❤❡♠❛ ❞✐ ❋✐❣✉r❛ ✷✳✶✵✱ ✉♥♦ ♥❡❧❧✬❛♠❜✐❡♥t❡

s❡♠✐❝♦♥✜♥❛t♦✱ s1✱ ❧✬❛❧tr♦ ✱ s2✱ ♥❡❧❧♦ s♣❛③✐♦ ❛♣❡rt♦ ❝r❡❛t♦ ❞❛❧❧✬✐♥t❡rr✉③✐♦♥❡ ❞❡❧❧❛ str✉tt✉r❛

✭❋✐❣✉r❛ ✶✳✶✮✱ s✐ s♦♥♦ ❝♦❧❧❡③✐♦♥❛t✐ ✐♥ ❢✉♥③✐♦♥❡ ❞❡❧ t❡♠♣♦ ✐ ✈❛❧♦r✐ ❞✐ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ t♦t❛❧❡

s♦tt♦✱ I0,C ✱ ❡ ❢✉♦r✐ ❞❛❧❧❛ ❝♦♣❡rt✉r❛✱ I0✱ ❡ ❝♦♥ ❧❡ ❡q✉❛③✐♦♥✐ ♣r❡s❡♥t❛t❡ ♥❡❧ P❛r❛❣r❛❢♦ ✷✳✹✳✸ s✐

è ❞✐✈✐s❛ ❧❛ r❛❞✐❛③✐♦♥❡ ♥❡❧❧❡ ❝♦♠♣♦♥❡♥t✐ ❞✐r❡tt❛ I0,b ❡ ❞✐✛✉s❛ I0,d✳

✷✹

❋✐❣✉r❛ ✷✳✶✵✿ ❙❝❤❡♠❛ s❡③✐♦♥❡ ❧♦♥❣✐t✉❞✐♥❛❧❡ ❞❡❧❧❛ ❝♦♣❡rt✉r❛ ✐♥ ♣r♦ss✐♠✐tà ❞❡❧❧✬✐♥t❡rr✉③✐♦♥❡

❉❡tt♦ t ✐❧ ❝♦❡✣❝✐❡♥t❡ ❞✐ tr❛s♠✐ss✐♦♥❡ ❞❡❧ ✈❡tr♦ ❢✉♥③✐♦♥❡ ❞❡❧❧✬❛♥❣♦❧♦ ❞✐ ✐♥❝✐❞❡♥③❛ ❞❡❧❧❛

r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ❞✐r❡tt❛ ❡ ♥❡❧❧✬✐♣♦t❡s✐ r❛❣✐♦♥❡✈♦❧❡ ❝❤❡ ❧❛ r❛❞✐❛③✐♦♥❡ ❞✐✛✉s❛ ✐♥❝✐❞❡♥t❡ s✉❧

s♦❧❛r✐♠❡tr♦✱ s2, s✐❛ ❧❛ st❡ss❛ ✐♥❝✐❞❡♥t❡ s✉❧ s♦❧❛r✐♠❡tr♦✱ s1✱ è ♣♦ss✐❜✐❧❡ s❝r✐✈❡r❡✿

I0,C = I0,bt+ I0,dt

I0 = I0,b + I0,dt

✭✷✳✷✺✮

❡ss❡♥❞♦✱

I0,d = kI0,b ✭✷✳✷✻✮

s♦st✐t✉❡♥❞♦ ♥❡❧❧❛ ✭✷✳✷✺✮✿

I0,C = I0,bt+ kI0,bt = t(1 + k)I0,b

I0 = I0,b + kI0,bt = (1 + kt)I0,b

✭✷✳✷✼✮

❝❤✐❛♠❛♥❞♦ t′ =I0,CI0

✱ s✐ ♦tt✐❡♥❡✿

t =t′

1 + k − kt′✭✷✳✷✽✮

✷✺

❙✐ ♦tt✐❡♥❡ ❝♦sì ✐❧ ✈❛❧♦r❡ ❞❡❧ ❝♦❡✣❝✐❡♥t❡ ❞✐ tr❛s♠✐ss✐♦♥❡ ❞❡❧ ✈❡tr♦ ✐♥ ❢✉♥③✐♦♥❡ ❞❡❧ t❡♠♣♦

♦✈✈❡r♦ ✐♥ ❢✉♥③✐♦♥❡ ❞❡❧❧✬❛♥❣♦❧♦ ❞✐ ✐♥❝✐❞❡♥③❛ θ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ❞✐r❡tt❛ s✉❧❧❛ ❝♦♣❡rt✉r❛✳

■♥ ❋✐❣✉r❛ ✷✳✶✶ è r✐♣♦rt❛t♦ ❧✬❛♥❞❛♠❡♥t♦ ❞✐ θ ✐♥ ❢✉♥③✐♦♥❡ ❞❡❧ t❡♠♣♦✱ ♠❡♥tr❡ ✐♥ ❚❛❜❡❧❧❛ ✷✳✷

s♦♥♦ r✐♣♦rt❛t✐ ✐ ✈❛❧♦r✐ ❞✐ t ♠❡❞✐❛t✐ s✉ 5◦ ♣❡r θ ❝♦♠♣r❡s♦ tr❛ 25◦ ❡ 50◦ ♦tt❡♥✉t✐ ❞❛❧❧❡

♠✐s✉r❛③✐♦♥✐ ❞❡❧ ❣✐♦r♥♦ ✸✵ ▲✉❣❧✐♦ ✷✵✶✷ tr❛ ❧❡ ♦r❡ 11 : 00 ❡ ❧❡ ♦r❡ 14 : 45✳

❋✐❣✉r❛ ✷✳✶✶✿ ❆♥❣♦❧♦ ❞✐ ✐♥❝✐❞❡♥③❛ θ ✐♥ ❢✉♥③✐♦♥❡ ❞❡❧ t❡♠♣♦ ✭✸✵ ▲✉❣❧✐♦ ✷✵✶✷✮

❆♥❣♦❧♦ ❞✐ ✐♥❝✐❞❡♥③❛ θ(◦C) ❈♦❡✣❝✐❡♥t❡ ❞✐ tr❛s♠✐ss✐♦♥❡ t

25 0.350

30 0.333

35 0.316

40 0.322

45 0.320

50 0.324

❚❛❜❡❧❧❛ ✷✳✷✿ ❱❛❧♦r✐ ♠❡❞✐ ❞❡❧ ❝♦❡✣❝✐❡♥t❡ ❞✐ tr❛s♠✐ss✐♦♥❡ t ❞❡❧❧❛ ❝♦♣❡rt✉r❛ ✐♥ ❢✉♥③✐♦♥❡❞❡❧❧✬❛♥❣♦❧♦ ❞✐ ✐♥❝✐❞❡♥③❛ ✭♠✐s✉r❡ ❞❡❧ ✸✵ ▲✉❣❧✐♦ ✷✵✶✷✮

✷✻

❈♦♥s✐❞❡r❛♥❞♦ q✉✐♥❞✐ ✐ ✈❛❧♦r✐ ❝❛❧❝♦❧❛t✐ ❞❡❧ ❝♦❡✣❝✐❡♥t❡ ❞✐ tr❛s♠✐ss✐♦♥❡ t ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ s♦✲

❧❛r❡ ❞✐r❡tt❛ ❡ ❧❡ ❝❛r❛tt❡r✐st✐❝❤❡ ❡♥❡r❣❡t✐❝❤❡ ❡♠✐s❢❡r✐❝❤❡ ❞❡❧ s✐♥❣♦❧♦ ♣❛♥♥❡❧❧♦ ✐♥ ✈❡tr♦ ❢♦r♥✐t❡

❞❛❧ ❝♦str✉tt♦r❡ ✭❚❛❜❡❧❧❛ ✶✳✶✮ è ♣♦ss✐❜✐❧❡ ❝❛r❛tt❡r✐③③❛r❡ ❝♦♠♣❧❡t❛♠❡♥t❡ ✐❧ ❝♦♠♣♦rt❛♠❡♥✲

t♦ ❞❡❧❧❛ ❝♦♣❡rt✉r❛✿ ✐♥ ❚❛❜❡❧❧❛ ✷✳✸ s♦♥♦ r✐♣♦rt❛t❡ ❧❡ ♣r♦♣r✐❡tà ❡♠✐s❢❡r✐❝❤❡ ❞✐ tr❛s♠✐ss✐♦♥❡

❡❞ ❛ss♦r❜✐♠❡♥t♦ ❡❞ ✐♥ ❋✐❣✉r❛ ✷✳✶✷ s♦♥♦ r✐♣♦rt❛t❡ ❧❡ ♣r♦♣r✐❡tà ✐♥ ❢✉♥③✐♦♥❡ ❞❡❧❧✑❛♥❣♦❧♦ ❞✐

✐♥❝✐❞❡♥③❛ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ❞✐r❡tt❛ θ✳

❚r❛s♠✐ss✐♦♥❡ ❆ss♦r❜✐♠❡♥t♦

0.33 0.40

❚❛❜❡❧❧❛ ✷✳✸✿ ❱❛❧♦r✐ ❡♠✐s❢❡r✐❝✐ ❞✐ tr❛s♠✐ss✐♦♥❡ ❡❞ ❛ss♦r❜✐♠❡♥t♦ ❞❡❧❧❛ ❝♦♣❡rt✉r❛

❋✐❣✉r❛ ✷✳✶✷✿ ❈♦❡✣❝✐❡♥t❡ ❞✐ ❛ss♦r❜✐♠❡♥t♦ ❡ ❝♦❡✣❝✐❡♥t❡ ❞✐ tr❛s♠✐ss✐♦♥❡ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡s♦❧❛r❡ ❞✐r❡tt❛ ✐♥ ❢✉♥③✐♦♥❡ ❞❡❧❧✬❛♥❣♦❧♦ ❞✐ ✐♥❝✐❞❡♥③❛

✷✼

✷✳✻ ❈❛❧❝♦❧♦ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡ ✐♥ ❝❛s♦ ❞✐ s♦❣❣❡tt♦

❡s♣♦st♦ ❛❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡

▲♦ s♣❛③✐♦ s❡♠✐❝♦♥✜♥❛t♦ ♦❣❣❡tt♦ ❞✐ st✉❞✐♦✱ ♦❧tr❡ ❡ss❡r❡ ✐♥t❡r❡ss❛t♦ ❞❛❧❧♦ s❝❛♠❜✐♦ t❡r♠✐✲

❝♦ r❛❞✐❛t✐✈♦ ❛ ❜❛ss❛ ❢r❡q✉❡♥③❛ tr❛ ❧❡ s✉♣❡r✜❝✐ ✐♥t❡r♥❡✱ è ❝❛r❛tt❡r✐③③❛t♦ ❞❛❧❧❛ ♣r❡s❡♥③❛ ❞❡❧❧❛

r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ✭❞✐r❡tt❛ ❡ ❞✐✛✉s❛✮ ♦✈✈❡r♦ ❞❛ ✉♥❛ s♦r❣❡♥t❡ ✐rr❛❣❣✐❛♥t❡ ❛❞ ❛❧t❛ t❡♠♣❡r❛t✉r❛

❡ ❝♦♥ ✉♥❛ ❢♦rt❡ ❝♦♠♣♦♥❡♥t❡ ❞✐r❡③✐♦♥❛❧❡✳ ❈♦♠❡ ❝♦♥s❡❣✉❡♥③❛ s✐ ❤❛ ❝❤❡ ♣❡r ✐❧ ❝❛❧❝♦❧♦ ❞❡❧❧❛

t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡ tmr ❡ q✉✐♥❞✐ ♣❡r ❧❛ ✈❛❧✉t❛③✐♦♥❡ ❞❡❧❧❡ ❝♦♥❞✐③✐♦♥✐ ❞✐ ❝♦♠❢♦rt

t❡r♠✐❝♦ ♦❝❝♦rr❡ ✈❛❧✉t❛r❡ ❛♥❝❤❡ ✐❧ ❢❛tt♦r❡ ❞✬❛r❡❛ ♣r♦✐❡tt❛t❛ ❞❡❧ s♦❣❣❡tt♦ fp✳ ■♥❢❛tt✐ s❡❝♦♥❞♦

❣❧✐ st✉❞✐ ❞✐ ❋❛♥❣❡r ❬✼❪✱ ♣❡r ✈❛❧✉t❛r❡ ✐❧ ❝❛❧♦r❡ s❝❛♠❜✐❛t♦ ❞❛❧ ❝♦r♣♦ ✉♠❛♥♦ ❝♦♥ ❧❡ s✉♣❡r✜❝✐

✐♥ ✉♥ ❛♠❜✐❡♥t❡✱ ♦❝❝♦rr❡ ❝♦♥♦s❝❡r❡ tr❡ ❣r❛♥❞❡③③❡ ❣❡♦♠❡tr✐❝❤❡ ❢♦♥❞❛♠❡♥t❛❧✐✿

• ❢❛tt♦r❡ ❞✬❛r❡❛ ❞✐ r❛❞✐❛③✐♦♥❡ ❡✛❡tt✐✈❛✱ feff ✿ r❛♣♣r❡s❡♥t❛ ✐❧ r❛♣♣♦rt♦ tr❛ ❧❛ s✉♣❡r✜❝✐❡ ❞❡❧

❝♦r♣♦ ✈❡st✐t♦ ❡✛❡tt✐✈❛♠❡♥t❡ ✐♥t❡r❡ss❛t❛ ❛❧❧♦ s❝❛♠❜✐♦ r❛❞✐❛t✐✈♦ ✭Aeff ✮ ❡ ❧❛ s✉♣❡r✜❝✐❡

t♦t❛❧❡ ❞❡❧ ❝♦r♣♦ ✈❡st✐t♦ ✭Acl✮❀

• ❧✬❛r❡❛ ♣r♦✐❡tt❛t❛✱ Ap : ♦tt❡♥✉t❛ s♣❡r✐♠❡♥t❛❧♠❡♥t❡✱ è ❧✬❛r❡❛ ❞❡❧❧❛ ♣❡rs♦♥❛ ♣r♦✐❡tt❛t❛

s✉ ✉♥ ♣✐❛♥♦ ♣❡r♣❡♥❞✐❝♦❧❛r❡ ❛❧❧❛ ❞✐r❡③✐♦♥❡ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ ❞✐r❡tt❛❀

• ✐❧ ❢❛tt♦r❡ ❞✐ ❢♦r♠❛✱ FP−A✱ tr❛ ❧❛ ♣❡rs♦♥❛ ❝♦❧❧♦❝❛t❛ ✐♥ ✉♥ ♣✉♥t♦ P ❞✐ ❝✉✐ s♦♥♦ ♥♦t❡ ❧❡

❝♦♦r❞✐♥❛t❡ ❡❞ ✉♥❛ s✉♣❡r✜❝✐❡ A ❞❡❧❧✬❛♠❜✐❡♥t❡✿ r❛♣♣r❡s❡♥t❛ ❧❛ ❢r❛③✐♦♥❡ ❞✐ r❛❞✐❛③✐♦♥❡

❡♠❡ss❛ ❞❛❧❧❛ ♣❡rs♦♥❛ ❝❤❡ r❛❣❣✐✉♥❣❡ ❧❛ s✉♣❡r✜❝✐❡✳

◆❡❧ ❝❛s♦ ❞✐ ✉♥ ❛♠❜✐❡♥t❡ ♣r✐✈♦ ❞✐ ✉♥❛ s♦r❣❡♥t❡ ✐rr❛❣❣✐❛♥t❡ ❛❞ ❛❧t❛ ✐♥t❡♥s✐tà ✭❝♦♠❡ ✐❧ ❙♦❧❡✮✱

❧♦ s❝❛♠❜✐♦ t❡r♠✐❝♦ ♣❡r ✐rr❛❣❣✐❛♠❡♥t♦ tr❛ ✐❧ ❝♦r♣♦ ✉♠❛♥♦ ❡ ❧❡ s✉♣❡r✜❝✐ ❝✐r❝♦st❛♥t✐ s✐ ♣✉ò

❡s♣r✐♠❡r❡ ❝♦♠❡✿

RL = Aeffǫσ(T4

cl − T 4

mr) ✭✷✳✷✾✮

❞♦✈❡✿

T 4

mr =1

σ(B1FP−1 +B2FP−2 + ...+BNFP−N) ✭✷✳✸✵✮

✷✽

❞♦✈❡ Aeff è ❧❛ s✉♣❡r✜❝✐❡ ❞❡❧ ❝♦r♣♦ ✈❡st✐t♦ ❡✛❡tt✐✈❛♠❡♥t❡ ✐♥t❡r❡ss❛t❛ ❛❧❧♦ s❝❛♠❜✐♦ r❛❞✐❛✲

t✐✈♦✱ ǫ è ❧✬❡♠✐ss✐✈✐tà ❞❡❧❧❛ s✉♣❡r✜❝✐❡ ❡st❡r♥❛ ❞❡❧ ❝♦r♣♦ ✈❡st✐t♦✱ σ è ❧❛ ❝♦st❛♥t❡ ❞✐ ❙t❡❢❛♥

✲ ❇♦❧t③♠❛♥♥✱ Tcl è ❧❛ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ ❞❡❧❧❛ s✉♣❡r✜❝✐❡ ❡st❡r♥❛ ❞❡✐ ✈❡st✐t✐ ❡ Tmr è ❧❛

t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡✳ ▲✬❡q✉❛③✐♦♥❡ ✭✷✳✸✵✮ ❞❡✜♥✐s❝❡ ❧❛ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡

Tmr ♣❡r ❝♦r♣✐ ❣r✐❣✐ ❝♦♥ ❡♠✐ss✐✈✐tà ✉❣✉❛❧❡ ❛❧❧✬❛ss♦r❜✐♠❡♥t♦ ❡ ❝❛r❛tt❡r✐③③❛t✐ ❞❡❧ ❢❛tt♦ ❝❤❡

✐rr❛❣❣✐❛♥♦ ✭❡♠✐ss✐♦♥❡ ❡ r✐✢❡ss✐♦♥❡✮ ❝♦♥ r❛❞✐❛③✐♦♥❡ ❞✐✛✉s❛ ❡❞ ✐♥❞✐♣❡♥❞❡♥t❡ ❞❛❧❧❛ ❞✐r❡③✐♦♥❡✳

■ ♣❛r❛♠❡tr✐ Bi ✐♠♣✐❡❣❛t✐ ♥❡❧❧✬❡q✉❛③✐♦♥❡ ✭✷✳✸✵✮ r❛♣♣r❡s❡♥t❛♥♦ ❧❛ r❛❞✐❛③✐♦♥❡ ✐rr❛❣❣✐❛t❛ ❞❛❧❧❡

s✉♣❡r✜❝✐✱ s♦♠♠❛ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ ❡♠❡ss❛ ❡ r✐✢❡ss❛✿

B = ǫσT 4 + ρIs ✭✷✳✸✶✮

❞♦✈❡ ρ è ❧❛ r✐✢❡ss✐✈✐tà ❞❡❧❧❛ s✉♣❡r✜❝✐❡ ✭1− ǫ ♣❡r ❝♦r♣✐ ❣r✐❣✐✮ ❡ Is è ❧❛ r❛❞✐❛③✐♦♥❡ ❝❤❡ ✐♥❝✐❞❡

s✉❧❧❛ s✉♣❡r✜❝✐❡✳

P❡r ♠♦❧t✐ ♠❛t❡r✐❛❧✐ ❞❛ ❝♦str✉③✐♦♥❡ ❧❛ s✉♣❡r✜❝✐❡ ♣✉ò ❡ss❡r❡ ❛ss✉♥t❛ ❝♦♠❡ ❝♦r♣♦ ♥❡r♦ ❡❞

è ♣♦ss✐❜✐❧❡ tr❛s❝✉r❛r❡ ❧❛ ❝♦♠♣♦♥❡♥t❡ ❞✐ r❛❞✐❛③✐♦♥❡ r✐✢❡ss❛✳ ◗✉❡st♦ è ✐❧ ❝❛s♦ ❞✐ ❛♠❜✐❡♥t✐

❝♦♥✜♥❛t✐ ✐♥ ❝❛s♦ ❞✐ ❛ss❡♥③❛ ❞✐ ❢♦♥t✐ ❞✐ r❛❞✐❛③✐♦♥❡ ❛❞ ❛❧t❛ ✐♥t❡♥s✐tà ♣❡r ✐ q✉❛❧✐ è ♣♦ss✐❜✐❧❡

❝❛❧❝♦❧❛r❡ ❧❛ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡ Tmr ✐♠♣✐❡❣❛♥❞♦ ❧❛ r❡❧❛③✐♦♥❡ ❛♣♣r♦ss✐♠❛t❛✿

T 4

mr = T 4

1FP−1 + T 4

2FP−2 + ...+ T 4

NFP−N ✭✷✳✸✷✮

❞♦✈❡ Ti è ❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧❧❛ s✉♣❡r✜❝✐❡ i✲❡s✐♠❛ ❝❤❡ ❝♦st✐t✉✐s❝❡ ❧✬❛♠❜✐❡♥t❡ ❝♦♥✜♥❛t♦ ❡

FP−i ✐❧ ❢❛tt♦r❡ ❞✐ ❢♦r♠❛ tr❛ ✐❧ ❝♦r♣♦ ❞❡❧ s♦❣❣❡tt♦ ❡ ❧✬i✲❡s✐♠❛ s✉♣❡r✜❝✐❡ r✐❝❛✈❛❜✐❧❡ ❞❛✐ ❣r❛✜❝✐

❢♦r♥✐t✐ ❞❛ ❋❛♥❣❡r ❬✼❪ ❡ ❙t❡✐♥♠❛♥ ❡t ❛❧✳ ❬✷✷❪ ♣❡r s✉♣❡r✜❝✐ ✐♥❝❧✐♥❛t❡ ♦✈✈❡r♦✱ ♥❡❧ ♠♦❞❡❧❧♦✱

✐♠♣✐❡❣❛♥❞♦ ❧❡ r❡❧❛③✐♦♥✐ ❛♥❛❧✐t✐❝❤❡ ♦tt❡♥✉t❡ ❞❛ ❈❛♥♥✐str❛r♦ ❡t ❛❧✳ ❬✸❪✳

■❧ t❡r♠♠✐♥❡ Aeff ✱ ✐♠♣✐❡❣❛t♦ ♥❡❧❧✬❡q✉❛③✐♦♥❡ ✭✷✳✸✵✮✱ è ❞❡✜♥✐t♦✿

Aeff = fefffclADU =Aeff

Acl

·Acl

ADU

· ADU ✭✷✳✸✸✮

❞♦✈❡ fcl è ✐❧ ❢❛tt♦r❡ ❞✬❛r❡❛ ❞❡✐ ✈❡st✐t✐ ❝✐♦è ✐❧ r❛♣♣♦rt♦ tr❛ ❧✬❛r❡❛ ❞❡❧❧❛ s✉♣❡r✜❝✐❡ ❞❡❧ ❝♦r♣♦

❝♦♥ ✐ ✈❡st✐t✐ ❡ ❧✬❛r❡❛ ❞❡❧❛ s✉♣❡r✜❝✐❡ ❞❡❧ ❝♦r♣♦ s❡♥③❛ ✈❡st✐t✐ ❡ ADU è ❧✬❛r❡❛ ❞✐ ❉✉✲❇♦✐s

♦✈✈❡r♦ ❧✬❛r❡❛ ❞❡❧❧❛ s✉♣❡r✜❝✐❡ ❞❡❧ ❝♦r♣♦ ♣r✐✈❛ ❞✐ ✈❡st✐t✐✳ ▲❡ ✐♥❞❛❣✐♥✐ s♣❡r✐♠❡♥t❛❧✐ ❞✐ ❋❛♥❣❡r

✷✾

❤❛♥♥♦ ♣❡r♠❡ss♦ ❞✐ ✜ss❛r❡ ✐❧ ❢❛tt♦r❡ ❞✬❛r❡❛ ❞✐ r❛❞✐❛③✐♦♥❡ ❡✛❡tt✐✈❛✱ feff ✱ ♣❛r✐ ❛ 0.696 ♣❡r ❧❛

♣♦s✐③✐♦♥❡ s❡❞✉t❛ ❡ ♣❛r✐ ❛ 0.725 ♣❡r ❧❛ ♣♦s✐③✐♦♥❡ ✐♥ ♣✐❡❞✐✳ ❋❛♥❣❡r ❤❛ ❛♥❝❤❡ r✐❝❛✈❛t♦ ❞✉❡

❡q✉❛③✐♦♥✐ ♣❡r ✐❧ ❝❛❧❝♦❧♦ ❞✐fcl ✐♥ ❢✉♥③✐♦♥❡ ❞❡❧❧❛ r❡s✐st❡♥③❛ t❡r♠✐❝❛ ❞❡✐ ✈❡st✐t✐ Icl✿

fcl =

{

1.00 + 1.290Icl perIcl ≤ 0.078 m2◦❈/W

1.05 + 0.645Icl perIcl > 0.078 m2◦❈/W✭✷✳✸✹✮

❙❡ è ♣r❡s❡♥t❡ ✉♥❛ s♦r❣❡♥t❡ ❞✐ r❛❞✐❛③✐♦♥❡ ❛❞ ❛❧t❛ ✐♥t❡♥s✐tà✱ ❝♦♠❡ ❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ tr❛✲

s♠❡ss❛ ♥❡❧❧✬❛♠❜✐❡♥t❡ s❡♠✐❝♦♥✜♥❛t♦ ❛ttr❛✈❡rs♦ ❧❛ ❝♦♣❡rt✉r❛ ✐♥ ✈❡tr♦✱ ♣❡r ❝❛❧❝♦❧❛r❡ ❧❛ t❡♠✲

♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡ Tmr✱ ♣❡r ❝♦r♣✐ ♥♦♥ ❣r✐❣✐✱ ♦❝❝♦rr❡ r✐s♦❧✈❡r❡ ❧✬❡q✉❛③✐♦♥❡ ❞✐ ❜✐❧❛♥❝✐♦

❬✶✾❪✿

ǫpσAeff (T4

cl − T 4

mr) = ǫpσAeff (T4

cl − T 4

umr)− Apαrqr ✭✷✳✸✺✮

❞♦✈❡ Tumr è ❧❛ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡ ❞❡❧❧✬❛♠❜✐❡♥t❡ ✜tt✐③✐♦ ♣r✐✈♦ ❞✐ r❛❞✐❛③✐♦♥❡ ❛❞

❛❧t❛ ✐♥t❡♥s✐tà ❝❛❧❝♦❧❛❜✐❧❡ ❝♦♥ ❧✬❡q✉❛③✐♦♥❡ ✭✷✳✸✵✮✱ qr è ❧❛ ❞❡♥s✐tà ❞✐ ✢✉ss♦ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡

❛❞ ♦♥❞❛ ❜r❡✈❡ ✐♥❝✐❞❡♥t❡ s✉❧ s♦❣❣❡tt♦ ❡ αr è ✐❧ ❝♦❡✣❝✐❡♥t❡ ❞✐ ❛ss♦r❜✐♠❡♥t♦ ♠❡❞✐♦ ❞❡❧ ❝♦r♣♦

✉♠❛♥♦ ❝❤❡ ✈❛❧❡✱ ✐♥ ❝❛s♦ ❞✐ s♦r❣❡♥t❡ ✐rr❛❣❣✐❛♥t❡ ❛ 2500 K✱ 0.8 ❡ 0.65 ♣❡r ✐❧ ❝♦r♣♦ ✉♠❛♥♦

❝♦♥ ❡ s❡♥③❛ ✈❡st✐t✐✱ r✐s♣❡tt✐✈❛♠❡♥t❡✱ ❡❞ ✐♥ ❝❛s♦ ❞✐ s♦r❣❡♥t❡ ✐rr❛❣❣✐❛♥t❡ ❛ 1200 K✱ 0.9 ❡ 0.95

♣❡r ✐❧ ❝♦r♣♦ ✉♠❛♥♦ ❝♦♥ ❡ s❡♥③❛ ✈❡st✐t✐✱ r✐s♣❡tt✐✈❛♠❡♥t❡ ✭❘❛♣♣ ❡ ●❛❣❣❡ ❬✶✼✱ ✶✽❪✮✳

❆❧ ✜♥❡ ❞✐ r❡♥❞❡r❡ ✐♥❞✐♣❡♥❞❡♥t❡ ❧❛ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡ Tmr ❞❡❧❧❡ ❞✐♠❡♥s✐♦♥✐ ❞❡❧

s♦❣❣❡tt♦✱ s✐ ❞❡✜♥✐s❝❡ ✐❧ ❢❛tt♦r❡ ❞✬❛r❡❛ ♣r♦✐❡tt❛t❛ fp✿

fp =Ap

Aeff

✭✷✳✸✻✮

❡ s♦st✐t✉❡♥❞♦ ♥❡❧❧❛ ✭✷✳✸✺ ✮ s✐ ♦tt✐❡♥❡✿

Tmr = 4

√

T 4umr + fp

αrqrǫpσ

✭✷✳✸✼✮

✸✵

❋❛♥❣❡r ❤❛ r✐❝❛✈❛t♦ s♣❡r✐♠❡♥t❛❧♠❡♥t❡ ✐ ✈❛❧♦r✐ ❞❡❧ ❢❛tt♦r❡ ❞✬❛r❡❛ ♣r♦✐❡tt❛t❛ fp ♣❡r q✉❛ttr♦

❝♦♠❜✐♥❛③✐♦♥✐ ❞✐ ✈❡st✐t✐ ❡ ♣♦s✐③✐♦♥✐ ❞✐✈❡rs❡ s✐❛ ♣❡r s♦❣❣❡tt✐ ♠❛s❝❤✐❧✐ ❝❤❡ ❢❡♠♠✐♥✐❧✐✳ ■ ❢❛tt♦r✐

❞✬❛r❡❛ ♣r♦✐❡tt❛t❛ fp s♦♥♦ r✐♣♦rt❛t✐ ✐♥ ❣r❛✜❝✐ ✐♥ ❢✉♥③✐♦♥❡ ❞❡❧❧✬❛♥❣♦❧♦ ❞✐ ❛③✐♠✉t❤✱ α, ♣❡r

✈❛❧♦r✐ ❞✐s❝r❡t✐ ❛ss✉♥t✐ ❞❡❧❧✬❛♥❣♦❧♦ β ✭❋✐❣✉r❛ ✷✳✶✸ ✮✳

❋✐❣✉r❛ ✷✳✶✸✿ ●r❛♥❞❡③③❡ ✐♥t❡r❡ss❛t❡ ❛❧ ❝❛❧❝♦❧♦ ❞❡✐ ❢❛tt♦r✐ ❞✬❛r❡❛ ♣r♦✐❡tt❛t❛ fp ✭❞❛ P✳❖✳ ❋❛♥✲❣❡r✱ ❚❤❡r♠❛❧ ❈♦♠❢♦rt ✲ ❆♥❛❧②s✐s ❛♥❞ ❆♣♣❧✐❝❛t✐♦♥s ✐♥ ❊♥✈✐r♦♥♠❡♥t❛❧ ❊♥❣✐♥❡❡r✐♥❣✱ ❉❛♥✐s❤❚❡❝❤♥✐❝❛❧ Pr❡ss✱ ❈♦♣❡♥❤❛❣❡♥✱ ✶✾✼✵✮

❋❛♥❣❡r ❤❛ ❞❡t❡r♠✐♥❛t♦ s♣❡r✐♠❡♥t❛❧♠❡♥t❡ ❝♦♥ ✉♥ ♠❡t♦❞♦ ❢♦t♦❣r❛✜❝♦ ✐ ✈❛❧♦r✐ ❞✐ ❛r❡❛ ♣r♦✲

✐❡tt❛t❛ Ap ❡❞ ❡ss❡♥❞♦✿

Aeff =4

π

ˆ α=π

α=0

ˆ β=π/2

β=0

Ap cos βdαdβ ✭✷✳✸✽✮

❞❛❧❧✬❡q✉❛③✐♦♥❡ ✭✷✳✸✻ ✮ s✐ ❝❛❧❝♦❧❛♥♦ ✐ ✈❛❧♦r✐ ❞❡✐ ❢❛tt♦r✐ ❞✬❛r❡❛ ♣r♦✐❡tt❛t❛ fp✳ ❉❛❧ ♠♦♠❡♥t♦ ❝❤❡

❧✬❛❜❜✐❣❧✐❛♠❡♥t♦ ♥♦♥ ❤❛ ❛❧❝✉♥❛ ✐♥✢✉❡♥③❛ s✉❧ ✈❛❧♦r❡ ❛ss✉♥t♦ ❞❛ fp è ♣♦ss✐❜✐❧❡ r✐❛ss✉♠❡r❡ ✐

r✐s✉❧t❛t✐✱ ♠❡❞✐❛t✐ r✐s♣❡tt♦ s❡ss♦ ✭♠❛s❝❤✐❧❡ ❢❡♠♠✐♥✐❧❡✮ ❡❞ ❛❜❜✐❣❧✐❛♠❡♥t♦ ✭❝♦♥ ❡ s❡♥③❛ ✈❡st✐t✐✮✱

✐♥ ❞✉❡ ❣r❛✜❝✐✿ ✐❧ ❣r❛✜❝♦ ❞✐ ❋✐❣✉r❛ ✷✳✶✹ r✐♣♦rt❛ fp ✐♥ ❢✉♥③✐♦♥❡ ❞✐ α ❡ β ♣❡r ✐❧ s♦❣❣❡tt♦ ✐♥

♣♦s✐③✐♦♥❡ s❡❞✉t❛✱ ♠❡♥tr❡ ✐❧ ❣r❛✜❝♦ ❞✐ ❋✐❣✉r❛ ✷✳✶✺ r✐♣♦rt❛ fp ✐♥ ❢✉♥③✐♦♥❡ ❞✐ α ❡ β ♣❡r ✐❧

s♦❣❣❡tt♦ ✐♥ ♣✐❡❞✐✳

✸✶

✭❛✮ ✭❜✮

❋✐❣✉r❛ ✷✳✶✹✿ ❋❛tt♦r✐ ❞✬❛r❡❛ ♣r♦✐❡tt❛t❛ fp ♣❡r s♦❣❣❡tt♦ ✐♥ ♣♦s✐③✐♦♥❡ s❡❞✉t❛ ✭❛✮❀ ✐♥ ♣✐❡❞✐✭❜✮ ✭❞❛ P✳❖✳ ❋❛♥❣❡r✱ ❚❤❡r♠❛❧ ❈♦♠❢♦rt ✲ ❆♥❛❧②s✐s ❛♥❞ ❆♣♣❧✐❝❛t✐♦♥s ✐♥ ❊♥✈✐r♦♥♠❡♥t❛❧❊♥❣✐♥❡❡r✐♥❣✱ ❉❛♥✐s❤ ❚❡❝❤♥✐❝❛❧ Pr❡ss✱ ❈♦♣❡♥❤❛❣❡♥✱ ✶✾✼✵✮

▲✬✉t✐❧✐③③♦ ❞✐ ❣r❛✜❝✐ ♣❡r ❧❛ ✈❛❧✉t❛③✐♦♥❡ ❞✐ fp ❛❧❧✬✐♥t❡r♥♦ ❞✐ ✉♥❛ ♣r♦❣r❛♠♠❛ ❞✐ ❝❛❧❝♦❧♦ r✐s✉❧t❛

♣♦❝♦ ♣r❛t✐❝♦ ❡ s♦❣❣❡tt♦ ❛❞ ❡rr♦r✐ ❞✐ ❧❡tt✉r❛✳ ❘✐③③♦ ❡t ❛❧✳ ❬✶✾❪✱ s✉❧❧❛ ❜❛s❡ ❞❡✐ ❞❛t✐ s♣❡r✐✲

♠❡♥t❛❧✐ ❞✐ ❋❛♥❣❡r✱ ❤❛♥♥♦ s✈✐❧✉♣♣❛t♦ ❞✉❡ ❛❧❣♦r✐t♠✐ ♣♦❧✐♥♦♠✐❛❧✐ ♣❡r ✐❧ ❝❛❧❝♦❧♦ ❞❡❧❧❛ ❢✉♥③✐♦♥❡

fp = f(α, β) s✐❛ ♣❡r ✐❧ ❝❛s♦ ❞✐ s♦❣❣❡tt♦ ✐♥ ♣♦s✐③✐♦♥❡ s❡❞✉t❛✿

fp(α, β) =4∑

i=0

Ai(β) · αi ✭✷✳✸✾✮

❞♦✈❡✿

Ai(β) =3∑

j=0

Ai,j · βj ✭✷✳✹✵✮

s✐❛ ✐♥ ♣✐❡❞✐✿

fp(α, β) =4∑

i=0

Bi(β) · αi ✭✷✳✹✶✮

❞♦✈❡✿

✸✷

Bi(β) =3∑

j=0

Bi,j · βj ✭✷✳✹✷✮

✐ ❝♦❡✣❝✐❡♥t✐ Ai,j ❡ Bi,j s♦♥♦ r✐♣♦rt❛t✐ ✐♥ ❚❛❜❡❧❧❛ ✷✳✹✳

j i

0 1 2 3 4

Aij

0 +2.884 · 10−1 +2.225 · 10−3 −9.292 · 10−5 +9.027 · 10−7 −2.517 · 10−9

1 +2.225 · 10−3 −7.653 · 10−5 +4.021 · 10−6 −4.623 · 10−8 +1.380 · 10−10

2 −5.472 · 10−5 +7.286 · 10−7 −6.215 · 10−8 +7.690 · 10−10 −2.341 · 10−12

3 +1.802 · 10−7 −1.457 · 10−9 +3.152 · 10−10 −4.015 · 10−12 +1.231 · 10−14

Bij

0 +3.453 · 10−1 +1.945 · 10−3 −1.023 · 10−4 +1.003 · 10−6 −2.747 · 10−9

1 +6.930 · 10−4 +1.122 · 10−5 −1.502 · 10−7 +4.040 · 10−10 +8.461 · 10−13

2 −7.319 · 10−5 −1.288 · 10−6 +3.676 · 10−8 −3.036 · 10−10 +7.489 · 10−13

3 +3.675 · 10−7 +1.030 · 10−8 −2.517 · 10−10 +1.969 · 10−12 −4.715 · 10−15

❚❛❜❡❧❧❛ ✷✳✹✿ ❈♦❡✣❝✐❡♥t✐ Ai,j ❡ Bi,j ✐♠♣✐❡❣❛t✐ ✐♥ ✭✷✳✹✵ ✮ ❡ ✭✷✳✹✷ ✮ ✭❞❛ ●✳ ❘✐③③♦✱ ●✳ ❋r❛♥③✐tt❛✱●✳ ❈❛♥♥✐str❛r♦✱ ❆❧❣♦r✐t❤♠s ❢♦r t❤❡ ❝❛❧❝✉❧❛t✐♦♥ ♦❢ t❤❡ ♠❡❛♥ ♣r♦❥❡❝t❡❞ ❛r❡❛ ❢❛❝t♦rs ♦❢ s❡❛t❡❞❛♥❞ st❛♥❞✐♥❣ ♣❡rs♦♥s✱ ❊♥❡r❣② ❛♥❞ ❇✉✐❧❞✐♥❣s✱ ✈♦❧✳ ✶✼✱ ♣♣✳ ✷✷✶✕✷✸✵✱ ✶✾✾✶✮

■ ❢❛tt♦r✐ ❞✬❛r❡❛ ♣r♦✐❡tt❛t❛ fp ❝♦sì ❝❛❧❝♦❧❛t✐✱ ♣♦ss♦♥♦ ❡ss❡r❡ ✐♥tr♦❞♦tt✐ ♥❡❧❧✬❡q✉❛③✐♦♥❡ ✭✷✳✸✼ ✮✱

♦✈✈❡r♦ ♥❡❧❧✬❡q✉❛③✐♦♥❡ ✭✷✳✹✸✮ ❬✶✷❪ ❝❤❡ ❡s♣❧✐❝✐t❛ ✐ ❝♦♥tr✐❜✉t✐ r❛❞✐❛t✐✈✐ ♣r❡s❡♥t✐ ♥❡❧❧✬❛♠❜✐❡♥t❡

s❡♠✐❝♦♥✜♥❛t♦ ♦❣❣❡tt♦ ❞✐ ✐♥❞❛❣✐♥❡ ✭❋✐❣✉r❛ ✷✳✶✺ ✮✿

Tmr =

(

N∑

i=1

FP−iT4

i +αr,d

ǫpσ

M∑

j=1

FP−jId,j +αr,b

ǫpσfpIb

)1/4

✭✷✳✹✸✮

❞♦✈❡ FP−i/j s♦♥♦ ✐ ❢❛tt♦r✐ ❞✐ ❢♦r♠❛ tr❛ ✐❧ ❝♦r♣♦ ❞❡❧ s♦❣❣❡tt♦ ❡ ❧✬i✲❡s✐♠❛ s✉♣❡r✜❝✐❡ ❝❤❡

s✐ tr♦✈❛ ❛❧❧❛ t❡♠♣❡r❛t✉r❛ ❛ss♦❧✉t❛ Ti✱ ♦ tr❛ ✐❧ ❝♦r♣♦ ❞❡❧ s♦❣❣❡tt♦ ❡ ❧❛ j✲❡s✐♠❛ s✉♣❡r✜❝✐❡

✸✸

❞❛❧❧❛ q✉❛❧❡ ♣r♦✈✐❡♥❡ ❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ❞✐✛✉s❛ Id,j❀ αr,d è ✐❧ ❝♦❡✣❝✐❡♥t❡ ❞✐ ❛ss♦r❜✐♠❡♥t♦

❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ❞✐✛✉s❛ ♣❡r ✐❧ ❝♦r♣♦ ✉♠❛♥♦ ❛ss✉♥t♦ ♣❛r✐ ❛ 0.7❀ αr,b è ✐❧ ❝♦❡✣❝✐❡♥t❡

❞✐ ❛ss♦r❜✐♠❡♥t♦ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ❞✐r❡tt❛ ♣❡r ✐❧ ❝♦r♣♦ ✉♠❛♥♦ ❛ss✉♥t♦ ♣❛r✐ ❛ 0.7❀

ǫp è ✐❧ ❝♦❡✣❝✐❡♥t❡ ❞✐ ❡♠✐ss✐✈✐tà ♣❡r ✐❧ ❝♦r♣♦ ✉♠❛♥♦ ❛ss✉♥t♦ ♣❛r✐ ❛ 0.97✳ P❡r ❧♦ s♣❛③✐♦

s❡♠✐❝♦♥✜♥❛t♦ Ib è ❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ❞✐r❡tt❛ tr❛s♠❡ss❛ ❛ttr❛✈❡rs♦ ❧❛ ❝♦♣❡rt✉r❛ ✐♥ ✈❡tr♦✱

Id,j ❝♦♠♣r❡♥❞❡ ❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ❞✐✛✉s❛ tr❛s♠❡ss❛ ❛ttr❛✈❡rs♦ ❧❛ ❝♦♣❡rt✉r❛ ✐♥ ✈❡tr♦✱ ❧❛

r❛❞✐❛③✐♦♥❡ ❛❞ ♦♥❞❛ ❜r❡✈❡ r✐✢❡ss❛ ❞❛❧ ♣❛✈✐♠❡♥t♦ ❡ ❞❛❧❧❛ s✉♣❡r✜❝✐❡ ✐♥t❡r♥❛ ❞❡❧❧❛ ❝♦♣❡rt✉r❛

❡ ❧❛ r❛❞✐❛③✐♦♥❡ ❛❞ ♦♥❞❛ ❜r❡✈❡ ❝❤❡ ❡♥tr❛ ❞❛❧❧❡ ❞✉❡ ❛♣❡rt✉r❡ ❧❛t❡r❛❧✐ ❡ Ti è ❧❛ t❡♠♣❡r❛t✉r❛

❛ss♦❧✉t❛ ❝❤❡ ❝❛r❛tt❡r✐③③❛ ❧♦ s❝❛♠❜✐♦ t❡r♠✐❝♦ r❛❞✐❛t✐✈♦ ❛❞ ♦♥❞❛ ❧✉♥❣❛ ❝♦♥ ❧❛ s✉♣❡r✜❝❡

✐♥t❡r♥❛ ❞❡❧❧❛ ❝♦♣❡rt✉r❛✱ ✐❧ ❜❛s❛♠❡♥t♦ ❡❞ ❧❛ ♣♦r③✐♦♥❡ ❞✐ ❝✐❡❧♦ ✈✐st♦ ❞❛❧❧❡ ❛♣❡rt✉r❡ ❧❛t❡r❛❧✐✳

❋✐❣✉r❛ ✷✳✶✺✿ ❙❝❛♠❜✐ r❛❞✐❛t✐✈✐ tr❛ ❛♠❜✐❡♥t❡ s❡♠✐❝♦♥✜♥❛t♦ ❡ ❝♦r♣♦ ✉♠❛♥♦

✸✹

✷✳✼ ❇✐❧❛♥❝✐♦ ❡♥❡r❣❡t✐❝♦ ❞❡❧ ❝♦r♣♦ ✉♠❛♥♦ ❡❞ ✐♥❞✐❝❡ ❞✐ ❝♦♠❢♦rt

t❡r♠✐❝♦ P❊❚

▲❛ ❢♦r♠✉❧❛③✐♦♥❡ ❞✐ ✉♥ ✐♥❞✐❝❡ ❞✐ ❝♦♠❢♦rt t❡r♠✐❝♦ ❞❡✈❡ ❡ss❡r❡ ❜❛s❛t❛ s✉❧ ❜✐❧❛♥❝✐♦ ❡♥❡r✲

❣❡t✐❝♦ ❞❡❧ ❝♦r♣♦ ✉♠❛♥♦ ❝♦♥ ❧✬❛♠❜✐❡♥t❡ ❝✐r❝♦st❛♥t❡✳ ■❧ ♠♦❞❡❧❧♦ ❞✐ ✐♥t❡r❛③✐♦♥❡ t❡r♠✐❝❛ tr❛ ✐❧

❝♦r♣♦ ✉♠❛♥♦ ❡ ❧✬❛♠❜✐❡♥t❡✱ ♣✐ù s❡♠♣❧✐❝❡ ❡ ♥♦t♦✱ è ✐❧ ❝♦sì ❞❡tt♦ ♠♦❞❡❧❧♦ ❛ ❞✉❡ ♥♦❞✐ ✭●❛❣❣❡

❬✹❪✮ ❝❤❡ ❝♦♥s✐❞❡r❛ ✐❧ ❝♦r♣♦ ✉♠❛♥♦ ❝♦♠❡ ❞✉❡ ❝♦♠♣❛rt✐♠❡♥t✐ t❡r♠✐❝✐ ❝♦♥❝❡♥tr✐❝✐ ❝♦st✐t✉✐t✐

❞❛✐ t❡ss✉t✐ ❞✐ ♣❡❧❧❡ ❡ ❞❛❧❧✬✐♥t❡r♥♦ ❞❡❧ ❝♦r♣♦✱ r✐s♣❡tt✐✈❛♠❡♥t❡✳

❋✐❣✉r❛ ✷✳✶✻✿ ■♥t❡r❛③✐♦♥❡ tr❛ ❝♦r♣♦ ✉♠❛♥♦ ❡❞ ❛♠❜✐❡♥t❡ s❡❝♦♥❞♦ ✐❧ ♠♦❞❡❧❧♦ ❛ ❞✉❡ ♥♦❞✐✭❞❛ ❆❙❍❘❆❊ ❍❛♥❞❜♦♦❦✲❋✉♥❞❛♠❡♥t❛❧s✱ ❆♠❡r✐❝❛♥ ❙♦❝✐❡t② ♦❢ ❍❡❛t✐♥❣✱ ❘❡❢r✐❣❡r❛t✐♥❣ ❛♥❞❆✐r✲❈♦♥❞✐t✐♦♥✐♥❣ ❊♥❣✐♥❡❡rs✱ ■♥❝✳✱ ❆t❧❛♥t❛✱ ✷✵✵✶✮

■♥ ❝♦♥❞✐③✐♦♥✐ ❞✐ ❡q✉✐❧✐❜r✐♦✱ ✐❧ ❜✐❧❛♥❝✐♦ ❡♥❡r❣❡t✐❝♦ ❞❡❧ ❝♦r♣♦ ✉♠❛♥♦ è ❡s♣r❡ss♦ ❞❛✿

M −W = C +R + Esk + Cres + Eres

❞♦✈❡M ❡W s♦♥♦✱ r✐s♣❡tt✐✈❛♠❡♥t❡✱ ❧❛ ♣r♦❞✉③✐♦♥❡ ❞✐ ❝❛❧♦r❡ ♠❡t❛❜♦❧✐❝♦ ❡ ✐❧ ❧❛✈♦r♦ ♠❡❝❝❛♥✐❝♦

❝♦♠♣✐✉t♦❀ C ❡ R s♦♥♦✱ r✐s♣❡tt✐✈❛♠❡♥t❡✱ ✐❧ ❝❛❧♦r❡ s❡♥s✐❜✐❧❡ ♣❡rs♦ ❛ttr❛✈❡rs♦ ❧❛ ♣❡❧❧❡ ♣❡r

❝♦♥✈❡③✐♦♥❡ ❡ ♣❡r ✐rr❛❣❣✐❛♠❡♥t♦❀ Esk è ✐❧ ❝❛❧♦r❡ ♣❡rs♦ ♣❡r ❡✈❛♣♦r❛③✐♦♥❡ ❛ttr❛✈❡rs♦ ❧❛ ♣❡❧❧❡❀

Cres ❡ Eres s♦♥♦ ✐❧ ❝❛❧♦r❡ ♣❡rs♦ ❛ttr❛✈❡rs♦ ❧❛ r❡s♣✐r❛③✐♦♥❡ ♣❡r ❝♦♥✈❡③✐♦♥❡ ❡ ♣❡r ❡✈❛♣♦r❛③✐♦♥❡✱

r✐s♣❡tt✐✈❛♠❡♥t❡ ✳ ▲✬❡q✉❛③✐♦♥❡ ❞✐ ❜✐❧❛♥❝✐♦ ❞❡❧❧✬❡♥❡r❣✐❛ ✐♥❝❧✉❞❡ t✉tt✐ ✐ ♣❛r❛♠❡tr✐ r✐❣✉❛r❞❛♥t✐

❧❡ ❝♦♥❞✐③✐♦♥✐ ❝❧✐♠❛t✐❝❤❡ ❡ s♦❣❣❡tt✐✈❡✿ ❛tt✐✈✐tà✱ ❛❜❜✐❣❧✐❛♠❡♥t♦ ❡ ✜s✐♦❧♦❣✐❛✳ ▲❛ s♦❧✉③✐♦♥❡

❞✐ t❛❧❡ ❡q✉❛③✐♦♥❡ r✐❝❤✐❡❞❡ ✐❧ ❝❛❧❝♦❧♦✱ ♦❧tr❡ ❝❤❡ ❞❡❣❧✐ s❝❛♠❜✐ ❞✐ ❝❛❧♦r❡ ❡❞ ✐❧ tr❛s♣♦rt♦ ❞✐

✸✺

♠❛ss❛✱ ❞✐ t✉tt✐ ✐ ♣r♦❝❡ss✐ t❡r♠♦r❡❣♦❧❛t♦r✐ ❞✐ ❜❛s❡✱ ❝♦♠❡ ❧❛ ❝♦str✐③✐♦♥❡ ❡ ❧❛ ❞✐❧❛t❛③✐♦♥❡

❞❡✐ ✈❛s✐ s❛♥❣✉✐❣♥✐ ♣❡r✐❢❡r✐❝✐✱ ❧❛ s✉❞♦r❛③✐♦♥❡ ❡ ❧❛ tr❛s♣✐r❛③✐♦♥❡✳ ▲✬❡q✉❛③✐♦♥❡ ❞✐ ❜✐❧❛♥❝✐♦

❞❡❧❧✬❡♥❡r❣✐❛ ❞❡❧ ❝♦r♣♦ ✐♥ ❝♦♥❞✐③✐♦♥✐ ❞✐ ❡q✉✐❧✐❜r✐♦ è st❛t❛ r✐s♦❧t❛ ❜❛s❛♥❞♦s✐ s✉❧ ♠♦❞❡❧❧♦ ❛ ❞✉❡

♥♦❞✐ ▼❊▼■ ▼✉♥✐❝❤ ❊♥❡r❣② ❜❛❧❛♥❝❡ ▼♦❞❡❧ ❢♦r ■♥❞✐✈✐❞✉❛❧s ✭❍ö♣♣❡ ✶✾✽✹✮✱ ✐♠♣❧❡♠❡♥t❛t♦

♥❡❧ s♦❢t✇❛r❡ ❘❛②▼❛♥ ✶✳✷ ❬✷✵❪✱ ❝♦♥s✐❞❡r❛♥❞♦ ✐❧ s♦❣❣❡tt♦ ♣♦st♦ ✐♥ ♣✐❡❞✐ ❛❧ ❝❡♥tr♦ ❞❡❧❧♦ s♣❛③✐♦

s❡♠✐❝♦♥✜♥❛t♦✳

P❡r ❝❛r❛tt❡r✐③③❛r❡ ❧✬❛♠❜✐❡♥t❡ ❞❛❧ ♣✉♥t♦ ❞✐ ✈✐st❛ t❡r♠✐❝♦ s✐ è ✉t✐❧✐③③❛t♦ ❧✬✐♥❞✐❝❡ ❞✐ ❝♦♠❢♦rt

t❡r♠✐❝♦ P❊❚ P❤②s✐♦❧♦❣✐❝❛❧ ❊✛❡❝t✐✈❡ ❚❡♠♣❡r❛t✉r❡ ✭❍ö♣♣❡ ❬✶✵❪✮ ❜❛s❛t♦ s✉❧ ♠♦❞❡❧❧♦ ❛ ❞✉❡

♥♦❞✐ ▼❊▼■ ❡ ❞❡✜♥✐t♦ ❝♦♠❡ ✏❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧❧✬❛r✐❛ ❞✐ ✉♥ ❛♠❜✐❡♥t❡ ❝♦♥✜♥❛t♦ ✜tt✐③✐♦

✭❛ss❡♥③❛ ❞✐ ✈❡♥t♦ ❡ ❞✐ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡✮ ♥❡❧ q✉❛❧❡ s✐ ❤❛ ✐❧ r❛❣❣✐✉♥❣✐♠❡♥t♦ ❞❡❧❧✬❡q✉✐❧✐❜r✐♦

t❡r♠✐❝♦ ❝♦♥ t❡♠♣❡r❛t✉r❛ ❞❡✐ t❡ss✉t✐ ✐♥t❡r♥✐ ❡ ❞❡❧❧❛ ♣❡❧❧❡ ✉❣✉❛❧✐ ❛ q✉❡❧❧❡ ❝❤❡ s✐ ❤❛♥♥♦ s♦tt♦

❧❡ ❝♦♥❞✐③✐♦♥✐ ❞❡❧❧✬❛♠❜✐❡♥t❡ t❡r♠✐❝♦ r❡❛❧❡ ♦❣❣❡tt♦ ❞✐ ❝❛r❛tt❡r✐③③❛③✐♦♥❡✑✳ ▲✬❛♠❜✐❡♥t❡ ❝♦♥✜✲

♥❛t♦ ✜tt✐③✐♦ è ❛ss✉♥t♦ ❝♦♥ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡ ✉❣✉❛❧❡ ❛❧❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧❧✬❛r✐❛✱

✈❡❧♦❝✐tà ❞❡❧❧✬❛r✐❛ ♣❛r✐ ❛ 0.1 m/s ❡ ♣r❡ss✐♦♥❡ ♣❛r③✐❛❧❡ ❞✐ ✈❛♣♦r❡ ❞✐ 12 hPa✳ ■❧ P❊❚ è ✐♥✲

❞✐♣❡♥❞❡♥t❡ ❞❛ ♣❛r❛♠❡tr✐ s♦❣❣❡tt✐✈✐ ♣♦✐❝❤è✱ ♥❡❧❧❛ s✉❛ ❞❡✜♥✐③✐♦♥❡✱ s✐❛ ❧✬❛tt✐✈✐tà s✈♦❧t❛ ❞❛❧

s♦❣❣❡tt♦ ❝❤❡ ❧❛ r❡s✐st❡♥③❛ t❡r♠✐❝❛ ❞❡✐ ✈❡st✐t✐ ✐♥❞♦ss❛t✐ s♦♥♦ ✜ss❛t✐ ❛❞ ✉♥ ✈❛❧♦r❡ ❝♦st❛♥t❡

♣❛r✐ ❛ 80 W ✭❛tt✐✈✐tà ❧❡❣❣❡r❛✮ ❡ 0.9 clo ✭clo è ❧✬✉♥✐tà ❞✐ ♠✐s✉r❛ ✐♥❝♦❡r❡♥t❡ ♣❡r ❧❛ r❡s✐st✐✈✐tà

t❡r♠✐❝❛ ❞❡❧❧✬❛❜❜✐❣❧✐❛♠❡♥t♦ ❬✶❪✮✱ r✐s♣❡tt✐✈❛♠❡♥t❡✳ ■♥ ❚❛❜❡❧❧❛ ✷✳✻ s✐ r✐♣♦rt❛ ❧❛ ❝♦rr❡❧❛③✐♦♥❡

tr❛ ♣❡r❝❡③✐♦♥❡ ❞❡❧❧✬❛♠❜✐❡♥t❡ t❡r♠✐❝♦ ❡❞ ✐♥❞✐❝❡ P❊❚✳

PET ◦C Percezione dell′ambiente termico

48131823293541

♠♦❧t♦ ❢r❡❞❞♦❢r❡❞❞♦❢r❡s❝♦

❧❡❣❣❡r♠❡♥t❡ ❢r❡s❝♦❝♦♠❢♦rt

❧❡❣❣❡r♠❡♥t❡ t✐❡♣✐❞♦t✐❡♣✐❞♦❝❛❧❞♦

♠♦❧t♦ ❝❛❧❞♦

❚❛❜❡❧❧❛ ✷✳✺✿ ❈♦rr❡❧❛③✐♦♥❡ tr❛ ♣❡r❝❡③✐♦♥❡ ❞❡❧❧✬❛♠❜✐❡♥t❡ t❡r♠✐❝♦ ❡❞ ✐♥❞✐❝❡ P❊❚

✸✻

■♥ ❚❛❜❡❧❧❛ ✷✳✻ s✐ r✐♣♦rt❛♥♦ ❛❧❝✉♥✐ ❡s❡♠♣✐ s✐❣♥✐✜❝❛t✐✈✐ ❞✐ ❛♠❜✐❡♥t✐ t❡r♠✐❝✐ ❝❛r❛tt❡r✐③③❛t✐

s❡❝♦♥❞♦ ❧✬✐♥❞✐❝❡ ❞✐ ❝♦♠❢♦rt t❡r♠✐❝♦ P❊❚✳

Ambiente Ta◦C Tmr

◦C W (m/s) pv(hPa) PET ◦C

Confinato 21 21 0.1 12 21

Invernale, soleggiato −5 40 0.5 2 10

Invernale, coperto −5 −5 5 2 −13

Estativo, soleggiato 30 60 1 21 43

Estativo, coperto 30 30 1 21 29

❚❛❜❡❧❧❛ ✷✳✻✿ ❊s❡♠♣✐ ❞✐ ❛♣♣❧✐❝❛③✐♦♥❡ ❞❡❧❧✬✐♥❞✐❝❡ P❊❚

■❧ P❊❚✱ ❡ss❡♥❞♦ ❜❛s❛t♦ s✉ ✉♥ ♠♦❞❡❧❧♦ t❡r♠♦✜s✐♦❧♦❣✐❝♦ ❞✐ ❜✐❧❛♥❝✐♦ ❞❡❧❧✬❡♥❡r❣✐❛✱ ❢♦r♥✐s❝❡

✉♥❛ ✈❛❧✉t❛③✐♦♥❡ r❡❛❧❡ ❞❡❧❧❛ s❡♥s❛③✐♦♥❡ t❡r♠✐❝❛ ♣❡r❝❡♣✐t❛ ❞❛✐ s♦❣❣❡tt✐ ❡❞ è st❛t♦ ❝♦♥❝❡♣✐t♦

♣r❡✈❛❧❡♥t❡♠❡♥t❡ ♣❡r ❝❛r❛tt❡r✐③③❛r❡ ❛♠❜✐❡♥t✐ t❡r♠✐❝✐ s❡♠✐❝♦♥✜♥❛t✐ ❡❞ ❛♣❡rt✐ ♣♦✐❝❤è ♠❡tt❡

✐♥ ❡✈✐❞❡♥③❛ ❣❧✐ ❡✛❡tt✐ s✐❛ ❞❡❧❧❡ ♦♥❞❡ ❝♦rt❡ ✭✐♥ ♣❛rt✐❝♦❧❛r❡ ❧❛ r❛❞✐❛③✐♦♥❡ ♣r♦✈❡♥✐❡♥t❡ ❞❛❧ s♦❧❡✮

❝❤❡ ❞❡❧❧❡ ♦♥❞❡ ❧✉♥❣❤❡ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ t❡r♠✐❝❛✳

❖❝❝♦rr❡ t✉tt❛✈✐❛ ♣r❡❝✐s❛r❡ ❝❤❡ ✐❧ P❊❚ ♥♦♥ ❝♦st✐t✉✐s❝❡ ✉♥❛ ✈❛❧✉t❛③✐♦♥❡ ❛ss♦❧✉t❛ ❞❡❧❧❡ ❝♦♥✲

❞✐③✐♦♥✐ ❞✐ ❝♦♠❢♦rt t❡r♠✐❝♦ s♦♣r❛tt✉tt♦ ♥❡❧❧✬❛♥❛❧✐s✐ ❞✐ ❛♠❜✐❡♥t✐ s❡♠✐❝♦♥✜♥❛t✐ ❡❞ ❛♣❡rt✐✳ ❆

q✉❡st♦ r✐❣✉❛r❞♦✱ ❙♣❛❣♥♦❧♦ ❡ ❞❡ ❉❡❛r ❬✷✶❪✱ st✉❞✐❛♥❞♦ ❧❡ ❝♦♥❞✐③✐♦♥✐ ❞✐ ❝♦♠❢♦rt t❡r♠✐❝♦ ♣❡r

✉♥ ❡❧❡✈❛t♦ ♥✉♠❡r♦ ❞✐ ❛♠❜✐❡♥t✐ ❡st❡r♥✐ ❡ s❡♠✐❝♦♥✜♥❛t✐✱ ❝♦♥❝❧✉s❡r♦ ❝❤❡ ❧❛ ❢❛s❝✐❛ ❞✐ ❝♦♠✲

❢♦rt t❡r♠✐❝♦ è s✐❣♥✐✜❝❛t✐✈❛♠❡♥t❡ ♣✐ù ❛♠♣✐❛ ♣❡r ❛♠❜✐❡♥t✐ ❡st❡r♥✐ ❡ s❡♠✐❝♦♥✜♥❛t✐ r✐s♣❡tt♦

❝❤❡ ♣❡r ❛♠❜✐❡♥t✐ ❝♦♥✜♥❛t✐✳ ◗✉❡st♦ ❛❝❝❛❞❡ ♣♦✐❝❤è ✐ s♦❣❣❡tt✐ ♣♦st✐ ✐♥ ❛♠❜✐❡♥t✐ ❡st❡r♥✐ ❡

s❡♠✐❝♦♥✜♥❛t✐ s❡♥t♦♥♦ ✉♥❛ ♠❛❣❣✐♦r❡ ✈❛r✐❛❜✐❧✐tà ❞❡❧❧❡ ❝♦♥❞✐③✐♦♥✐ t❡r♠✐❝❤❡ ❛♠❜✐❡♥t❛❧✐ ♥❡❧❧♦

s♣❛③✐♦ ❡ ♥❡❧ t❡♠♣♦✱ r✐s♣❡tt♦ q✉❛♥t♦ ♥♦♥ ❛✈✈❡♥❣❛ ✐♥ ❛♠❜✐❡♥t✐ ❝♦♥✜♥❛t✐✱ ❡ ♣❡r❝❡♣✐s❝♦♥♦

❛ss❡♥③❛ ❞✐ ❝♦♥tr♦❧❧♦ ❞❡❧❧❡ ❝♦♥❞✐③✐♦♥✐ ♠✐❝r♦❝❧✐♠❛t✐❝❤❡✳ ■♥♦❧tr❡ ❍ö♣♣❡ ❬✾❪ ❤❛ ❡✈✐❞❡♥③❛t♦

❝❤❡ ❧❛ ✈❛❧✉t❛③✐♦♥❡ ❞❡❧ ❝♦♠❢♦rt t❡r♠✐❝♦ ✐♥ ❛♠❜✐❡♥t✐ ❡st❡r♥✐ ❡ s❡♠✐❝♦♥✜♥❛t✐ r✐❝❤✐❡❞❡r❡❜❜❡

✉♥ ❛❧tr♦ ♠♦❞❡❧❧♦ ♣❡r ❧♦ st✉❞✐♦ ❞❡❧❧❡ ❝♦♥❞✐③✐♦♥✐ ❞✐ ♥♦♥ ❡q✉✐❧✐❜r✐♦ ♣♦✐❝❤è s♦❧✐t❛♠❡♥t❡ t❛❧✐

❛♠❜✐❡♥t✐ ✈❡♥❣♦♥♦ ♦❝❝✉♣❛t✐ ❞❛❧❧❡ ♣❡rs♦♥❡ ♣❡r t❡♠♣✐ ❜r❡✈✐ ♦ ❝♦♠✉♥q✉❡ ✐♥ ❝♦♥❞✐③✐♦♥✐ tr❛♥✲

✸✼

s✐t♦r✐❡✱ ♣❡rt❛♥t♦ ✐ ♠♦❞❡❧❧✐ ❞✐ t❡r♠♦r❡❣♦❧❛③✐♦♥❡ ❝♦r♣♦r❡❛ ✐♥ ❝♦♥❞✐③✐♦♥✐ ❞✬❡q✉✐❧✐❜r✐♦ t❡♥❞♦♥♦

❛ s♦✈r❛st✐♠❛r❡ ✐❧ ❞✐s❝♦♠❢♦rt ♣❡r ✐♥t❡r✈❛❧❧✐ ❞✐ t❡♠♣♦ ❞✐ ❡s♣♦s✐③✐♦♥❡ ❛❞ ❛♠❜✐❡♥t✐ ❡st❡r♥✐ ♦

s❡♠✐❝♦♥✜♥❛t✐ ✐♥❢❡r✐♦r✐ ❛❞ ✉♥✬♦r❛✳

✸✽

✸ ❙tr✉♠❡♥t✐ ♣❡r ❧❛ ♠✐s✉r❛ ❞❡❧❧❡ ❣r❛♥❞❡③③❡ ✜s✐❝❤❡

❙❡❣✉❡ ❧❛ ❞❡s❝r✐③✐♦♥❡ ❞❡✐ ♣r✐♥❝✐♣✐ ✜s✐❝✐ ❞✐ ❢✉♥③✐♦♥❛♠❡♥t♦ ❡ ❞❡❧❧❛ ♠❡ss❛ ✐♥ ♦♣❡r❛ ❞❡❣❧✐

str✉♠❡♥t✐ ✐♠♣✐❡❣❛t✐ ❞✉r❛♥t❡ ❧❛ ❝❛♠♣❛❣♥❛ ❞✐ ♠✐s✉r❡✳

✸✳✶ ▼✐s✉r❛ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧❧✬❛r✐❛

▲❛ ♠✐s✉r❛ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧❧✬❛r✐❛ s✐ ♦tt✐❡♥❡ ♣❛rt❡♥❞♦ ❞❛❧❧❛ r✐❧❡✈❛③✐♦♥❡ ❞✐ ❣r❛♥❞❡③③❡

✜s✐❝❤❡ ❝❤❡ s♦♥♦ ❢✉♥③✐♦♥✐ ❝♦♥t✐♥✉❡ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ st❡ss❛✱ ❛❞ ❡s❡♠♣✐♦ ❧✉♥❣❤❡③③❡ ❞✐ s♦❧✐❞✐✱

✈♦❧✉♠✐ ❞✐ ❧✐q✉✐❞✐✱ r❡s✐st❡♥③❛ ❡❧❡ttr✐❝❛ ❡ ❢♦r③❛ ❡❧❡ttr♦♠♦tr✐❝❡✳ ❉❛❧ ♠♦♠❡♥t♦ ❝❤❡ ✉♥ s❡♥s♦r❡

♠✐s✉r❛ ❧❛ t❡♠♣❡r❛t✉r❛ ❛❧❧❛ q✉❛❧❡ ❡ss♦ st❡ss♦ s✐ tr♦✈❛ ❡ q✉❡st❛ ♣✉ò ❡ss❡r❡ ♠♦❧t♦ ❞✐✈❡rs❛ ❞❛❧❧❛

t❡♠♣❡r❛t✉r❛ ❞❡❧ ✢✉✐❞♦ ❞❛ ♠✐s✉r❛r❡ ✭❛r✐❛ ♥❡❧ ❝❛s♦ ✐♥ ❡s❛♠❡✮✱ r✐s✉❧t❛ ♥❡❝❡ss❛r✐♦ ❛❞♦tt❛r❡

❛❧❝✉♥❡ ♣r❡❝❛✉③✐♦♥✐ ♣❡r r✐❞✉rr❡ ❧✬❡rr♦r❡✳

■♥ ♣❛rt✐❝♦❧❛r❡ s✐ ❞❡✈❡ ❧✐♠✐t❛r❡ ❧✬❡s♣♦s✐③✐♦♥❡ ❞❡❧❧❛ s♦♥❞❛ ❛❧❧❛ r❛❞✐❛③✐♦♥❡ ♣r♦✈❡♥✐❡♥t❡ ❞❛❧ s♦❧❡

❡ ❞❛ s♦r❣❡♥t✐ ❞✐ ❝❛❧♦r❡✱ ✐♥ ❝❛s♦ ❝♦♥tr❛r✐♦ ❧❛ t❡♠♣❡r❛t✉r❛ ♠✐s✉r❛t❛ r✐s✉❧t❡r❡❜❜❡ ♣❛r✐ ❛❞ ✉♥

✈❛❧♦r❡ ✐♥t❡r♠❡❞✐♦ tr❛ ❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧❧✬❛r✐❛ ❡ ❧❛ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡✳ ◗✉✐ s✐

r✐♣♦rt❛♥♦ ❛❧❝✉♥❡ s♦❧✉③✐♦♥✐ tr❛tt❡ ❞❛❧❧❛ ❧❡tt❡r❛t✉r❛ t❡❝♥✐❝❛ ✭❬✶❪✱❬✷✸❪✮ ♣❡r ❛❜❜❛ss❛r❡ ❧✬❡✛❡tt♦

❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ s✉❧❧❛ s♦♥❞❛✿

• r✐❞✉rr❡ ❧✬❡♠✐ss✐✈✐tà ❞❡❧ s❡♥s♦r❡ ✐♠♣✐❡❣❛♥❞♦ ✉♥❛ s♦♥❞❛ ❝♦♥ s✉♣❡r✜❝✐❡ ✐♥ ♠❡t❛❧❧♦ ❧✉❝✐✲

❞❛t♦ ♦ r✐❝♦♣❡rt❛ ❝♦♥ ✈❡r♥✐❝❡ r✐✢❡tt❡♥t❡❀

• r❡❛❧✐③③❛r❡ ✉♥ s❡♥s♦r❡ ❞✐ ♣✐❝❝♦❧❡ ❞✐♠❡♥s✐♦♥✐ ♣♦✐❝❤è ❛❧ ❞✐♠✐♥✉✐r❡ ❞❡❧❧❡ ❞✐♠❡♥s✐♦♥✐ ❞❡❧

s❡♥s♦r❡✱ ✐❧ ❝♦❡✣❝✐❡♥t❡ ❞✐ s❝❛♠❜✐♦ t❡r♠✐❝♦ ♣❡r ❝♦♥✈❡③✐♦♥❡ ❛✉♠❡♥t❛✱ ♠❡♥tr❡ ✐❧ ❝♦❡✣✲

❝✐❡♥t❡ ❞✐ s❝❛♠❜✐♦ t❡r♠✐❝♦ ♣❡r ✐rr❛❣❣✐❛♠❡♥t♦ r❡st❛ ❝♦st❛♥t❡❀ ✐♥♦❧tr❡ ✉♥ s❡♥s♦r❡ ❞✐ ♣✐❝✲

❝♦❧❡ ❞✐♠❡♥s✐♦♥✐ ❛✈rà ❛♥❝❤❡ ✉♥✬✐♥❡r③✐❛ t❡r♠✐❝❛ ♠✐♥♦r❡ ❝❤❡ ❝♦♥s❡♥t❡ t❡♠♣✐ ❞✐ r✐s♣♦st❛

♣✐ù ❜❛ss✐❀

✸✾

• s❝❤❡r♠❛r❡ ❧❛ s♦♥❞❛ ❝♦♥ ❧❛str❡ ✐♥ ♠❡t❛❧❧♦ ❧✉❝✐❞❛t♦✱ ❛❞ ❡s❡♠♣✐♦ ❛❧❧✉♠✐♥✐♦✱ ❞✐ s♣❡ss♦r❡

s♦tt✐❧❡ ✭0.1÷0.2mm✮ ❡✱ s❡ ♥♦♥ s✐ ❞✐s♣♦♥❡ ✉♥ s✐st❡♠❛ ❞✐ ✈❡♥t✐❧❛③✐♦♥❡ ❢♦r③❛t❛✱ ❝♦♥✈✐❡♥❡

❧❛s❝✐❛r❡ ✉♥ ❝❡rt♦ s♣❛③✐♦ tr❛ s❡♥s♦r❡ ❡ ♣❛r❡t❡ ❞❡❧❧♦ s❝❤❡r♠♦ ♣❡r ♣❡r♠❡tt❡r❡ ❛❧❧✬❛r✐❛ ❞✐

❝✐r❝♦❧❛r❡ ✐♥t❡r♥❛♠❡♥t❡ ♣❡r ❝♦♥✈❡③✐♦♥❡ ♥❛t✉r❛❧❡❀

• ✐♠♣✐❡❣❛r❡ ✉♥ s✐st❡♠❛ ❞✐ ✈❡♥t✐❧❛③✐♦♥❡ ❢♦r③❛t❛ ✭♠❡❣❧✐♦ s❡ ❛s♣✐r❛♥t❡✮ ♣❡r ❛✉♠❡♥t❛r❡ ✐❧

❝♦❡✣❝✐❡♥t❡ ❞✐ s❝❛♠❜✐♦ t❡r♠✐❝♦ ♣❡r ❝♦♥✈❡③✐♦♥❡✳

■♥ ❋✐❣✉r❛ ✸✳✶ s✐ ♠♦str❛✱ ✐♥ ❢✉♥③✐♦♥❡ ❞❡❧❧❛ ✈❡❧♦❝✐tà ❞❡❧❧✬❛r✐❛ ❡ ❞❡❧ ❞✐❛♠❡tr♦ ❞❡❧ s❡♥s♦r❡✱ ❝♦♠❡

✈❛r✐❛ ❧✬✐♥✢✉❡♥③❛ r❡❧❛t✐✈❛ ❞❡❧❧❛ t❡r♠♣❡r❛t✉r❛ ❞❡❧❧✬❛r✐❛ r✐s♣❡tt♦ ❧✬❡✛❡tt♦ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛

♠❡❞✐❛ r❛❞✐❛♥t❡ s✉❧❧❛ ♠✐s✉r❛③✐♦♥❡ ❡✛❡tt✉❛t❛ ❝♦♥ ✉♥❛ s♦♥❞❛ ♥♦♥ s❝❤❡r♠❛t❛✳ ▲❛ t❡♠♣❡r❛t✉r❛

♠✐s✉r❛t❛ ❞❛❧ s❡♥s♦r❡ ♣✉ò ❡ss❡r❡ ❡s♣r❡ss❛ ❝♦♠❡✿

Tmisurata = x · Ta + (1− x) · Tmr ✭✸✳✶✮

❞♦✈❡ x è ❧✬✐♥✢✉❡♥③❛ r❡❧❛t✐✈❛ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧❧✬❛r✐❛ Ta ❡ Tmr è ❧❛ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛

r❛❞✐❛♥t❡✳ ■ r✐s✉❧t❛t✐ r✐♣♦rt❛t✐ ✐♥ ❋✐❣✉r❛ ✸✳✶ s♦♥♦ st❛t✐ ♦tt❡♥✉t✐ ❝♦♥s✐❞❡r❛♥❞♦ ❧✬❡♠✐ss✐✈✐tà

❞❡❧ s❡♥s♦r❡ ♣❛r✐ ❛ 0.95✳

❋✐❣✉r❛ ✸✳✶✿ ■♥✢✉❡♥③❛ r❡❧❛t✐✈❛ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧❧✬❛r✐❛ s✉❧❧❛ t❡♠♣❡r❛t✉r❛ ♠✐s✉r❛t❛❞❛❧ s❡♥s♦r❡ ✐♥ ❢✉♥③✐♦♥❡ ❞✐ ✈❡❧♦❝✐tà ❞❡❧❧✬❛r✐❛ ❡ ❞✐❛♠❡tr♦ ❞❡❧❧❛ s♦♥❞❛ ✭❞❛ ❊◆ ■❙❖ ✼✼✷✻✱❊r❣♦♥♦♠✐❝s ♦❢ t❤❡ t❤❡r♠❛❧ ❡♥✈✐r♦♥♠❡♥t ✐♥str✉♠❡♥ts ❢♦r ♠❡❛s✉r✐♥❣ ♣❤②s✐❝❛❧ q✉❛♥t✐t✐❡s✱✷✵✵✶✮

✹✵

◗✉❛♥❞♦ s✐ ❡✛❡tt✉❛♥♦ ♠✐s✉r❡ ❞✐ t❡♠♣❡r❛t✉r❛ ♦❝❝♦rr❡ t❡♥❡r ❝♦♥t♦ ❛♥❝❤❡ ❞❡❧❧✬✐♥❡r③✐❛ t❡r♠✐❝❛

❞❡❧ s❡♥s♦r❡✳ ■♥❢❛tt✐ ✉♥ t❡r♠♦♠❡tr♦ ♣♦st♦ ✐♥ ✉♥ ❝❡rt♦ ❛♠❜✐❡♥t❡ ♥♦♥ ✐♥❞✐❝❛ ❧❛ t❡♠♣❡r❛t✉r❛

✐st❛♥t❛♥❡❛ ❞❡❧❧✬❛r✐❛✱ ♠❛ r✐❝❤✐❡❞❡ ✉♥ ❝❡rt♦ ♣❡r✐♦❞♦ ❞✐ t❡♠♣♦ ♣❡r r❛❣❣✐✉❣❡r❡ ❧✬❡q✉✐❧✐❜r✐♦

t❡r♠✐❝♦✳ ❯♥❛ ♠✐s✉r❛ ❞✐ t❡♠♣❡r❛t✉r❛ r✐s✉❧t❛ s✐❣♥✐✜❝❛t✐✈❛ s❡ r❡❣✐str❛t❛ ♥♦♥ ♣r✐♠❛ ❝❤❡

s✐❛ tr❛s❝♦rs♦ ✉♥ ♣❡r✐♦❞♦ ✉❣✉❛❧❡ ❛❞ ❛❧♠❡♥♦ 1.5 ✈♦❧t❡ ✐❧ t❡♠♣♦ ❞✐ r✐s♣♦st❛ ❞❡❧❧❛ s♦♥❞❛✳ ❯♥

t❡r♠♦♠❡tr♦ r✐s♣♦♥❞❡ t❛♥t♦ ♣✐ù r❛♣✐❞❛♠❡♥t❡ q✉❛♥t♦ ♣✐ù ✐❧ s❡♥s♦r❡ ❞✐ t❡♠♣❡r❛t✉r❛ è ♣✐❝❝♦❧♦

❡ ❧❡❣❣❡r♦ ❡ ❧❛ s✉❛ ❝❛♣❛❝✐tà t❡r♠✐❝❛ è ❜❛ss❛ ❡❞ è ❛❧t♦ ✐❧ ❝♦❡✣❝✐❡♥t❡ ❞✐ s❝❛♠❜✐♦ t❡r♠✐❝♦ ♣❡r

❝♦♥✈❡③✐♦♥❡✳

❊s✐st♦♥♦ ✈❛r✐❡ t✐♣♦❧♦❣✐❡ ❞✐ s❡♥s♦r✐✿ t❡r♠♦♠❡tr✐ ❛❞ ❡s♣❛♥s✐♦♥❡ ❛ ❧✐q✉✐❞♦ ✭❡s✳ ♠❡r❝✉r✐♦✮

♦ ❛ s♦❧✐❞♦❀ t❡r♠♦♠❡tr✐ ❡❧❡ttr✐❝✐ ❛ r❡s✐st❡♥③❛ ✈❛r✐❛❜✐❧❡ ✭r❡s✐st♦r✐✱ t❡r♠✐st♦r✐✮ ♦ ❜❛s❛t✐ s✉❧❧❛

❣❡♥❡r❛③✐♦♥❡ ❞✐ ✉♥❛ ❢♦r③❛ ❡❧❡ttr♦♠♦tr✐❝❡ ✭t❡r♠♦❝♦♣♣✐❡✮❀ t❡r♠♦♠❛♥♦♠❡tr✐ ❝❤❡ ♠✐s✉r❛♥♦ ❧❛

✈❛r✐❛③✐♦♥❡ ❞❡❧❧❛ ♣r❡ss✐♦♥❡ ❞✐ ✉♥ ❧✐q✉✐❞♦ ✐♥ ❢✉♥③✐♦♥❡ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛✳

◆❡❧❧❛ ❝❛♠♣❛❣♥❛ ❞✐ ♠✐s✉r❡✱ ♣❡r r✐❧❡✈❛r❡ ❧✬❛♥❞❛♠❡♥t♦ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧❧✬❛r✐❛ ❛❧ ❞✐ s♦t✲

t♦ ❞❡❧❧❛ ❝♦♣❡rt✉r❛✱ è st❛t❛ ✐♠♣✐❡❣❛t❛ ❧❛ s♦♥❞❛ ❝♦♠❜✐♥❛t❛ t❡♠♣❡r❛t✉r❛✲✉♠✐❞✐tà r❡❧❛t✐✈❛

❉❡❧t❛❖❍▼ ❍P✸✷✶✼ ❝♦❧❧❡❣❛t❛ ❛❧❧❛ ❝❡♥tr❛❧✐♥❛ ❞✐ ❛❝q✉✐s✐③✐♦♥❡ ❞❡✐ ♣❛r❛♠❡tr✐ ♠✐❝r♦❝❧✐♠❛t✐❝✐

❉❡❧t❛❖❍▼ ❍❉✸✷✳✶✳ ■❧ s❡♥s♦r❡ è ✉♥❛ t❡r♠♦r❡s✐st❡♥③❛ ❞✐ t✐♣♦ Pt✶✵✵ ❛ ✜❧♠ s♦tt✐❧❡ ❛❧ ♣❧❛t✐♥♦✿

❧❡ s♣❡❝✐✜❝❤❡ s♦♥♦ r✐♣♦rt❛t❡ ✐♥ ❚❛❜❡❧❧❛ ✸✳✶✳

❘❛♥❣❡ ❞✐ ♠✐s✉r❛ −200÷+650◦❈

❘✐s♦❧✉③✐♦♥❡ 0.01◦❈ ♥❡❧ ❝❛♠♣♦ ±199.99◦❈✱ 0.1◦❈ ♥❡❧ r❡st❛♥t❡ ❝❛♠♣♦

❆❝❝✉r❛t❡③③❛ ±0.01◦❈ ♥❡❧ ❝❛♠♣♦ ±199.99◦❈✱ ±0.1◦❈ ♥❡❧ r❡st❛♥t❡ ❝❛♠♣♦

■♥❝❡rt❡③③❛ ❞✐ ♠✐s✉r❛ ❈❧❛ss❡ 1/3 ❉■◆ ✭❉■◆ ✹✸✼✻✵✮

❚❡♠♣♦ ❞✐ r✐s♣♦st❛ T95 15′

❉✐♠❡♥s✐♦♥✐ 2 mm × 5 mm ✭❢♦r♠❛ r❡tt❛♥❣♦❧❛r❡✮

❉❡r✐✈❛ ✐♥ t❡♠♣❡r❛t✉r❛ @20◦❈ 0.003%/◦❈

❚❛❜❡❧❧❛ ✸✳✶✿ ❙♣❡❝✐✜❝❤❡ t❡❝♥✐❝❤❡ ❞❡❧ s❡♥s♦r❡ Pt✶✵✵ ❞❡❧❧❛ s♦♥❞❛ ❉❡❧t❛❖❍▼ ❍P✸✷✶✼

✹✶

❆❧ ✜♥❡ ❧✐♠✐t❛r❡ ❧✬❡✛❡tt♦ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ❡ r✐❞✉rr❡ ✐❧ t❡♠♣♦ ❞✐ r✐s♣♦st❛✱ s✐ è ♣r♦✈✈❡❞✉t♦

❛ s❝❤❡r♠❛r❡ ✐❧ s❡♥s♦r❡ ♣♦♥❡♥❞♦❧♦ ❛❧❧✬✐♥t❡r♥♦ ✉♥ t✉❜♦ ❞✐ ❞✐❛♠❡tr♦ 6.5 cm r✐❝♦♣❡rt♦ ❞❛ ✉♥♦

str❛t♦ ❞✐ ❛❧❧✉♠✐♥✐♦ ❧✉❝✐❞♦ ❡ s✐ è ✐♥st❛❧❧❛t❛ ✉♥❛ ✈❡♥t♦❧❛ ❛s♣✐r❛♥t❡✱ ❛❧✐♠❡♥t❛t❛ ❛ ❜❛tt❡r✐❛✱

s✉❧❧✬❡str❡♠✐tà s✉♣❡r✐♦r❡ ❛♣❡rt❛ ❞❡❧ t✉❜♦ ✭❋✐❣✉r❛ ✸✳✷✮✳

✭❛✮ ✭❜✮

❋✐❣✉r❛ ✸✳✷✿ ❙♦♥❞❛ ❞✐ t❡♠♣❡r❛t✉r❛ ❉❡❧t❛❖❍▼ ❍P✸✷✶✼ ✭❛✮❀ ❙♦♥❞❛ ❝♦♥ s❝❤❡r♠❛t✉r❛ ❡✈❡♥t♦❧❛ ❛s♣✐r❛♥t❡ ✐♥ s♦♠♠✐tà ✭❜✮

✹✷

✸✳✷ ▼✐s✉r❛ ❞❡❧❧✬✉♠✐❞✐tà r❡❧❛t✐✈❛

▲✬✉♠✐❞✐tà r❡❧❛t✐✈❛ r❛♣♣r❡s❡♥t❛ ✐❧ r❛♣♣♦rt♦ tr❛ ❧❛ q✉❛♥t✐tà ❡✛❡tt✐✈❛ ❞✐ ✈❛♣♦r❡ ❛❝q✉❡♦

♣r❡s❡♥t❡ ♥❡❧❧✬❛r✐❛ ❛♠❜✐❡♥t❡ ❡ ❧❛ ♠❛ss✐♠❛ q✉❛♥t✐tà ❝❤❡✱ ❛❧❧❛ ♠❡❞❡s✐♠❛ t❡♠♣❡r❛t✉r❛✱ s❛✲

r❡❜❜❡ ♥❡❝❡ss❛r✐❛ ♣❡r❝❤é ❧✬❛r✐❛ ❢♦ss❡ s❛t✉r❛✳ ❙✐ ❞❡✜♥✐s❝❡ q✉✐♥❞✐ ❧✬✉♠✐❞✐tà r❡❧❛t✐✈❛ ✭❣r❛❞♦

✐❣r♦♠❡tr✐❝♦ ϕ✮ ❝♦♠❡ ✐❧ r❛♣♣♦rt♦ tr❛ ❧❛ ♣r❡ss✐♦♥❡ ♣❛r③✐❛❧❡ ❞❡❧ ✈❛♣♦r ❞✬❛❝q✉❛ pv ♥❡❧❧✬❛r✐❛ ❡

❧❛ ♣r❡ss✐♦♥❡ ❞✐ s❛t✉r❛③✐♦♥❡ ❞❡❧ ✈❛♣♦r ❞✬❛❝q✉❛ ps(T ) ❛❧❧❛ st❡ss❛ t❡♠♣❡r❛t✉r❛✳

ϕ =pv

ps(T )✭✸✳✷✮

▲✬✉♠✐❞✐tà r❡❧❛t✐✈❛ ❘❍ è s♣❡ss♦ ❡s♣r❡ss❛ ❝♦♠❡ ♣❡r❝❡♥t✉❛❧❡✿

RH = 100 · ϕ ✭✸✳✸✮

P❡r ♠✐s✉r❛r❡ ❧✬✉♠✐❞✐tà r❡❧❛t✐✈❛ ❞❡❧❧✬❛r✐❛ ❛♠❜✐❡♥t❡ s✐ ✐♠♣✐❡❣❛♥♦ str✉♠❡♥t✐ ❝❤✐❛♠❛t✐ ✐❣r♦✲

♠❡tr✐✳ ❊s✐st♦♥♦ ❞✐✈❡rs❡ t✐♣♦❧♦❣✐❡ ❞✐ ✐❣r♦♠❡tr✐ ❝❤❡ s❢r✉tt❛♥♦ ♣r✐♥❝✐♣✐ ✜s✐❝✐ ❞✐✛❡r❡♥t✐✱ s✐

r✐♣♦rt❛♥♦ ❛❧❝✉♥✐ ❡s❡♠♣✐✳

▲✬✐❣r♦♠❡tr♦ ❛ ❝❛♣❡❧❧♦✱ ♦r♠❛✐ ❝❛❞✉t♦ ✐♥ ❞✐s✉s♦✱ è st❛t♦ ✐❧ ♣r✐♠♦ t✐♣♦ ❞✐ ✐❣r♦♠❡tr♦ ❛❞ ❡ss❡r❡

❝♦♥❝❡♣✐t♦✳ ❙✐ ❜❛s❛ s✉❧❧❛ ❞❡❢♦r♠❛③✐♦♥❡ ❞✐ ♣❛rt✐❝♦❧❛r✐ ♠❛t❡r✐❛❧✐ ♦r❣❛♥✐❝✐ ✭t✐♣♦ ❝❛♣❡❧❧✐✮ ❝❛✉✲

s❛t❛ ❞❛❧❧❛ t❡♥s✐♦♥❡ s✉♣❡r✜❝✐❛❧❡ ❞❡❧❧✬❛❝q✉❛ ♥❡✐ ♣♦r✐ ❞✐ q✉❡st✐ ♠❛t❡r✐❛❧✐✳ ■❧ ❝❛♣❡❧❧♦ ✉♠❛♥♦

✐♥❢❛tt✐ ♣r❡s❡♥t❛ ✉♥ ❛❧❧✉♥❣❛♠❡♥t♦ ❞✐ ❝✐r❝❛ ✐❧ 2.5 % ❢r❛ ❧♦ 0 ❡❞ ✐❧ 100 % ❞✐ ✉♠✐❞✐tà r❡❧❛t✐✲

✈❛✳ ▲❛ ✈❛r✐❛③✐♦♥❡ ❞✐ ❧✉♥❣❤❡③③❛ ♥♦♥ è ❡s❛tt❛♠❡♥t❡ ♣r♦♣♦r③✐♦♥❛❧❡ ✐♥ ♠♦❞♦ ❧✐♥❡❛r❡ r✐s♣❡tt♦

❛❧❧✬✉♠✐❞✐tà r❡❧❛t✐✈❛ ❡ r✐s✉❧t❛ ♥❡❝❡ss❛r✐♦ ❛♠♣❧✐✜❝❛r❡ ❝♦♥ ✉♥ s✐st❡♠❛ ❞✐ ❧❡✈❡ ♠❡❝❝❛♥✐❝❤❡ ✐❧

s❡❣♥❛❧❡ ✐♥ ✉s❝✐t❛✳ ▲♦ str✉♠❡♥t♦ ♥♦♥ r✐s✉❧t❛ ♣r❡❝✐s♦ ❡ ♣✉ò ❝♦♠♣♦rt❛r❡ ❡rr♦r✐ ❞❡❧ 5 ÷ 10

% ✐♥ ♣❛rt❡ ❝♦rr❡❣❣✐❜✐❧✐ ❝♦♥ ♦♣♣♦rt✉♥❡ t❛❜❡❧❧❡ ❝❤❡ r❡♥❞♦♥♦ ❝♦♥t♦ ❞❡❧❧❛ ♥♦♥ ❧✐♥❡❛r✐tà ❞❡❧❧❛

✈❛r✐❛③✐♦♥❡ ❞❡❧❧❛ ❧✉♥❣❤❡③③❛ ❞❡✐ ❝❛♣❡❧❧✐✳ ■♥♦❧tr❡ ❧✬❡rr♦r❡ ❞✐♣❡♥❞❡ ❞❛❧❧❛ t❡♠♣❡r❛t✉r❛ ❛ ❝✉✐ s✐

♦♣❡r❛ ❡❞ ❛❧ ❞✐ s♦tt♦ ❞❡✐ −30 ◦❈ ❧♦ str✉♠❡♥t♦ ♥♦♥ ❢✉♥③✐♦♥❛ ❛✛❛tt♦✳

▲♦ ♣s✐❝r♦♠❡tr♦✱ ♦ ✐❣r♦♠❡tr♦ ❞✐ ❆ss♠❛♥✱ s❢r✉tt❛ ❧✬❛❜❜❛ss❛♠❡♥t♦ ❞✐ t❡♠♣❡r❛t✉r❛ ❞❡❧❧✬❛r✐❛

❝❛✉s❛t♦ ❞❛❧❧✬❡✈❛♣♦r❛③✐♦♥❡ ❞❡❧❧✬❛❝q✉❛ s❡♥③❛ ❛♣♣♦rt♦ ❞✐ ❝❛❧♦r❡ ❞❛❧❧✬❡st❡r♥♦✳ ❚❛❧❡ t❡♠♣❡r❛t✉✲

✹✸

r❛ ✭✇❡t✲❜✉❧❜ t❡♠♣❡r❛t✉r❡✮ ✈✐❡♥❡ r✐❧❡✈❛t❛ ❞❛ ✉♥ t❡r♠♦♠❡tr♦ ❛ ❜✉❧❜♦✱ ❞❡tt♦ ❛ ❜✉❧❜♦ ✉♠✐❞♦✱

♣♦st♦ ❛ ❝♦♥t❛tt♦ ❝♦♥ ✉♥❛ ❣❛r③❛ ❜❛❣♥❛t❛ ❡ ✈✐❡♥❡ ❝♦♥❢r♦♥t❛t❛ ❝♦♥ ❧❛ t❡♠♣❡r❛t✉r❛ ♠✐s✉r❛t❛

❝♦♥ ✉♥ ❛♥❛❧♦❣♦ t❡r♠♦♠❡tr♦✱ ❞❡tt♦ ❛ ❜✉❧❜♦ ❛s❝✐✉tt♦✱ ❝❤❡ ♠✐s✉r❛ ❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧❧✬ ❛r✐❛

❛♠❜✐❡♥t❡ ✭❞r②✲❜✉❧❜ t❡♠♣❡r❛t✉r❡✮ ✳ ▲❛ t❡♠♣❡r❛t✉r❛ ❞✐ ❜✉❧❜♦ ❜❛❣♥❛t♦ è t❛♥t♦ ♠✐♥♦r❡ ❞❡❧❧❛

t❡♠♣❡r❛t✉r❛ ❞✐ ❜✉❧❜♦ ❛s❝✐✉tt♦ q✉❛♥t♦ ♣✐ù è ✐♥t❡♥s❛ ❧❛ ✈❛♣♦r✐③③❛③✐♦♥❡ ♦✈✈❡r♦ q✉❛♥t♦ ♣✐ù

❧✬❛r✐❛ ✐♥ ✐♥❣r❡ss♦ è s❡❝❝❛✳ ❊♥tr❛♥❞♦ ❝♦♥ q✉❡st✐ ❞✉❡ ✈❛❧♦r✐ ❞✐ t❡♠♣❡r❛t✉r❛ ♥❡❧ ❞✐❛❣r❛♠♠❛

♣s✐❝r♦♠❡tr✐❝♦ ✭❆♣♣❡♥❞✐❝❡ ❇✮ è ♣♦ss✐❜✐❧❡ st✐♠❛r❡ ❧✬✉♠✐❞✐tà r❡❧❛t✐✈❛ ❞❡❧❧✬❛r✐❛ ❛♠❜✐❡♥t❡✳ ▲♦

♣s✐❝r♦♠❡tr♦ è ❧♦ str✉♠❡♥t♦ ♣✐ù ♣r❡❝✐s♦ tr❛ q✉❡❧❧✐ q✉✐ ♣r❡s❡♥t❛t✐✳

▲✬✐❣r♦♠❡tr♦ ❡❧❡ttr♦♥✐❝♦ ✉t✐❧✐③③❛ s❡♥s♦r✐ ❛❧❧♦ st❛t♦ s♦❧✐❞♦ ❝❤❡ ♣♦ss✐❡❞♦♥♦ ❧❛ ❝❛r❛tt❡r✐st✐❝❛ ❞✐

✈❛r✐❛r❡ ✐ ♣r♦♣r✐ ♣❛r❛♠❡tr✐ ❡❧❡ttr✐❝✐ ✐♥ ❢✉♥③✐♦♥❡ ❞❡❧ ✈❛❧♦r❡ ❞✐ ✉♠✐❞✐tà r❡❧❛t✐✈❛ ❝✉✐ s♦♥♦ ❡s♣♦st✐✳

◗✉❡st♦ str✉♠❡♥t♦ è ❝♦st✐t✉✐t♦ ❞❛ ✉♥ tr❛s❞✉tt♦r❡ ❝❤❡ ♣✉ò ❡ss❡r❡ ❞✐ t✐♣♦ r❡s✐st✐✈♦ ♦ ❝❛♣❛❝✐t✐✈♦

❡ ❞❛❧ ❝✐r❝✉✐t♦ ❞✐ ❝♦♥❞✐③✐♦♥❛♠❡♥t♦ ❝❤❡✱ ✐♥ ❡♥tr❛♠❜✐ ✐ ❝❛s✐✱ ✉t✐❧✐③③❛ ✉♥❛ ❝♦♥✜❣✉r❛③✐♦♥❡ ❛

P♦♥t❡ ❞✐ ❲❤❡❛tst♦♥❡ ❝♦♥✈❡rt❡♥❞♦ ❧❛ ✈❛r✐❛③✐♦♥❡ r❡s✐st✐✈❛ ♦ ❝❛♣❛❝✐t✐✈❛ ✐♥ ✉♥ s❡❣♥❛❧❡ ❡❧❡ttr✐❝♦

♠✐s✉r❛❜✐❧❡✳ ▲✬✐❣r♦♠❡tr♦ ❡❧❡ttr♦♥✐❝♦ è ♣r❡❝✐s♦✱ ❝♦♠♣❛tt♦ ❡❞ ✐❧ s❡❣♥❛❧❡ ❡❧❡ttr✐❝♦ ✐♥ ✉s❝✐t❛ è

❢❛❝✐❧❡ ❞❛ tr❛tt❛r❡ ❡❞ ❛❝q✉✐s✐r❡ ❝♦♥ ✉♥❛ ❝❡♥tr❛❧✐♥❛ ❡❧❡ttr♦♥✐❝❛✳

◆❡❧❧❛ ❝❛♠♣❛❣♥❛ ❞✐ ♠✐s✉r❡✱ ♣❡r r✐❧❡✈❛r❡ ❧✬❛♥❞❛♠❡♥t♦ ❞❡❧❧✬✉♠✐❞✐tà r❡❧❛t✐✈❛ ❛❧ ❞✐ s♦tt♦ ❞❡❧❧❛

❝♦♣❡rt✉r❛✱ è st❛t❛ ✐♠♣✐❡❣❛t❛ ❧❛ s♦♥❞❛ ❝♦♠❜✐♥❛t❛ t❡♠♣❡r❛t✉r❛✲✉♠✐❞✐tà r❡❧❛t✐✈❛ ❉❡❧t❛❖❍▼

❍P✸✷✶✼ ❝♦❧❧❡❣❛t❛ ❛❧❧❛ ❝❡♥tr❛❧✐♥❛ ❞✐ ❛❝q✉✐s✐③✐♦♥❡ ❞❡✐ ♣❛r❛♠❡tr✐ ♠✐❝r♦❝❧✐♠❛t✐❝✐ ❉❡❧t❛❖❍▼

❍❉✸✷✳✶✳ ▲❛ s♦♥❞❛ ✐♥❝❧✉❞❡ ✉♥ s❡♥s♦r❡ ❝❛♣❛❝✐t✐✈♦ ❧❡ ❝✉✐ s♣❡❝✐✜❝❤❡ s♦♥♦ r✐♣♦rt❛t❡ ✐♥ ❚❛❜❡❧❧❛

✸✳✷✳

❘❛♥❣❡ ❞✐ ♠✐s✉r❛ 0÷ 100% RH

❘✐s♦❧✉③✐♦♥❡ 0.1% RH

❆❝❝✉r❛t❡③③❛ ±0.1% RH

■♥❝❡rt❡③③❛ ❞✐ ♠✐s✉r❛ ±2.5% RH

❉❡r✐✈❛ ✐♥ t❡♠♣❡r❛t✉r❛ @20◦❈ 0.02%UR/◦❈

❚❛❜❡❧❧❛ ✸✳✷✿ ❙♣❡❝✐✜❝❤❡ t❡❝♥✐❝❤❡ ❞❡❧ s❡♥s♦r❡ ❝❛♣❛❝✐t✐✈♦ ❞❡❧❧❛ s♦♥❞❛ ❉❡❧t❛❖❍▼ ❍P✸✷✶✼

✹✹

✸✳✸ ▼✐s✉r❛ ❞❡❧❧❛ ✈❡❧♦❝✐tà ❞❡❧❧✬❛r✐❛

❊s❡❣✉✐r❡ ♠✐s✉r❡ ❞❡❧❧❛ ✈❡❧♦❝✐tà ❞❡❧❧✬❛r✐❛ ✐♥ s♣❛③✐ ❛♣❡rt✐ è ♣✐✉tt♦st♦ ❝♦♠♣❧❡ss♦ ♣♦✐❝❤è

✐❧ ♠♦t♦ è t✉r❜♦❧❡♥t♦✱ s♦❣❣❡tt♦ ❛ ✢✉tt✉❛③✐♦♥✐ ❝❛s✉❛❧✐ ❡ ♠♦❧t♦ s♣❡ss♦ ❝❛♠❜✐❛ ❞✐r❡③✐♦♥❡✳

▲❛ ✈❡❧♦❝✐tà ❞❡❧❧✬❛r✐❛ va ♣✉ò ❡ss❡r❡ ❞❡t❡r♠✐♥❛t❛ ✐♠♣✐❡❣❛♥❞♦ ✉♥❛ s♦♥❞❛ ♦♠♥✐❞✐r❡③✐♦♥❛❧❡

♦✈✈❡r♦ s❡♥s✐❜✐❧❡ ❛❧❧❛ ✈❡❧♦❝✐tà q✉❛❧✉♥q✉❡ s✐❛ ❧❛ s✉❛ ❞✐r❡③✐♦♥❡ ♦♣♣✉r❡ ✉t✐❧✐③③❛♥❞♦ tr❡ s❡♥s♦r✐

❞✐r❡③✐♦♥❛❧✐ ❝❤❡ ♣❡r♠❡tt♦♥♦ ❞✐ ♠✐s✉r❛r❡ ❧❡ ❝♦♠♣♦♥❡♥t✐ ❞❡❧❧❛ ✈❡❧♦❝✐tà ❞❡❧❧✬❛r✐❛ ❧✉♥❣♦ ✐ tr❡

❛ss✐ ❝♦♦r❞✐♥❛t✐✳ ❈❤✐❛♠❛♥❞♦ vx, vy ❡ vz ❧❡ tr❡ ❝♦♠♣♦♥❡♥t✐ ❞✐ ✈❡❧♦❝✐tà✱ ❧❛ ✈❡❧♦❝✐tà ❞❡❧❧✬❛r✐❛

Va ♣✉ò ❡ss❡r❡ ❡s♣r❡ss❛ ❝♦♠❡✿

Va =√

v2x + v2y + v2z ✭✸✳✹✮

❊s✐st♦♥♦ ❞✐✈❡rs❡ t✐♣♦❧♦❣✐❡ ❞✐ str✉♠❡♥t✐✱ ❝❤✐❛♠❛t✐ ❛♥❡♠♦♠❡tr✐✱ ♣❡r ❧❛ ♠✐s✉r❛ ❞❡❧❧❛ ✈❡❧♦❝✐tà

❞❡❧❧✬❛r✐❛✿

❛♥❡♠♦♠❡tr♦ ❛ ❝♦♣♣❡tt❡✿ ♠✐s✉r❛ ❧❛ ✈❡❧♦❝✐tà ❞❡❧❧✬❛r✐❛ ❧✉♥❣♦ ✉♥✬✉♥✐❝❛ ❞✐r❡③✐♦♥❡❀

❛♥❡♠♦♠❡tr♦ ❛ ✜❧♦ ❝❛❧❞♦ ♦♠♥✐❞✐r❡③✐♦♥❛❧❡✿ s❡♥s✐❜✐❧❡ ❛❧❧❛ ✈❡❧♦❝✐tà q✉❛❧✉♥q✉❡ s✐❛ ❧❛ ❞✐r❡③✐♦♥❡❀

❛♥❡♠♦♠❡tr♦ ❛ ✜❧♦ ♣✉❧s❛♥t❡✿ ♦♠♥✐❞✐r❡③✐♦♥❛❧❡❀

❛♥❡♠♦♠❡tr♦ ❛❞ ✉❧tr❛s✉♦♥✐ ✿ ♦♠♥✐❞✐r❡③✐♦♥❛❧❡❀

❛♥❡♠♦♠❡tr♦ ❛ ❧❛s❡r✲❞♦♣♣❧❡r ✿ ♦♠♥✐❞✐r❡③✐♦♥❛❧❡✳

◆❡❧❧❛ ❝❛♠♣❛❣♥❛ ❞✐ ♠✐s✉r❡✱ ♣❡r r✐❧❡✈❛r❡ ❧❛ ✈❡❧♦❝✐tà ❞❡❧❧✬❛r✐❛ ❛❧ ❞✐ s♦tt♦ ❞❡❧❧❛ ❝♦♣❡rt✉r❛✱ è st❛✲

t♦ ✐♠♣✐❡❣❛t♦ ❧✬❛♥❡♠♦♠❡tr♦ ❛ ✜❧♦ ❝❛❧❞♦ ♦♠♥✐❞✐r❡③✐♦♥❛❧❡ ❉❡❧t❛❖❍▼ ❆P✸✷✵✸ ❝♦❧❧❡❣❛t♦ ❛❧❧❛

❝❡♥tr❛❧✐♥❛ ❞✐ ❛❝q✉✐s✐③✐♦♥❡ ❞❡✐ ♣❛r❛♠❡tr✐ ♠✐❝r♦❝❧✐♠❛t✐❝✐ ❉❡❧t❛❖❍▼ ❍❉✸✷✳✶✳ ▲❡ s♣❡❝✐✜❝❤❡

❞❡❧❧❛ s♦♥❞❛ s♦♥♦ r✐♣♦rt❛t❡ ✐♥ ❚❛❜❡❧❧❛ ✸✳✸✳

❙❡♥s♦r❡ t✐♣♦ NTC 10 kohm

❈❛♠♣♦ ❞✐ ♠✐s✉r❛ 0.05÷ 5 m/s

■♥❝❡rt❡③③❛ ❞✐ ♠✐s✉r❛ ±0.02 m/s (0.05÷ 1 m/s)✱ ±0.1 m/s (1÷ 5 m/s)

❚❛❜❡❧❧❛ ✸✳✸✿ ❙♣❡❝✐✜❝❤❡ t❡❝♥✐❝❤❡ ❞❡❧❧✬❛♥❡♠♦♠❡tr♦ ❛ ✜❧♦ ❝❛❧❞♦ ♦♠♥✐❞✐r❡③✐♦♥❛❧❡ ❉❡❧t❛❖❍▼❆P✸✷✵✸

✹✺

■❧ ♣r✐♥❝✐♣✐♦ ❞✐ ❢✉♥③✐♦♥❛♠❡♥t♦ ❞❡❧❧✬❛♥❡♠♦♠❡tr♦ ❛ ✜❧♦ ❝❛❧❞♦ s✐ ❜❛s❛ s✉❧❧♦ s❝❛♠❜✐♦ ❞✐ ❝❛❧♦r❡

❝❤❡ ❛✈✈✐❡♥❡ tr❛ ✐❧ ✜❧❛♠❡♥t♦ ✐♥ ❝✉✐ ❝✐r❝♦❧❛ ❝♦rr❡♥t❡ ❡❞ ✐❧ ✢✉✐❞♦ ❞✐ ❝✉✐ s✐ ❞❡✈❡ ❞❡t❡r♠✐♥❛r❡ ❧❛

✈❡❧♦❝✐tà✳ ◆❡❧ ✜❧♦ ❝♦♥❞✉tt♦r❡ ✈✐❡♥❡ ❢❛tt❛ ♣❛ss❛r❡ ✉♥❛ ❝♦rr❡♥t❡ I ❡❞ ✉t✐❧✐③③❛♥❞♦ ✉♥ ✈♦❧t♠❡tr♦

❡❞ ✉♥ ❛♠♣❡r♦♠❡tr♦ s✐ ♠✐s✉r❛ ✐❧ r❛♣♣♦rt♦ ❢r❛ ❧❛ t❡♥s✐♦♥❡ ❛✐ ❝❛♣✐ ❞❡❧ ✜❧♦ ∆V ❡ ❧❛ ❝♦rr❡♥t❡

I✱ è ♣♦ss✐❜✐❧❡ ❝♦sì ❝♦♥♦s❝❡r❡ ✐❧ ✈❛❧♦r❡ ❞❡❧❧❛ r❡s✐st❡♥③❛ ❡❧❡ttr✐❝❛ R✿

R =∆V

I✭✸✳✺✮

❊✬ ♥♦t♦ ❛♥❝❤❡ ❝❤❡ ❧❛ r❡s✐st❡♥③❛ ❡❧❡ttr✐❝❛ ❞✐ ✉♥ ❝♦♥❞✉tt♦r❡ ♦❤♠✐❝♦ ❞✐♣❡♥❞❡ ✐♥ ♠♦❞♦ ❧✐♥❡❛r❡

❞❛❧❧❛ t❡♠♣❡r❛t✉r❛ ✭R = R(T )✮✱ q✉✐♥❞✐ è ♣♦ss✐❜✐❧❡ ❞❡t❡r♠✐♥❛r❡ ❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧ ✜❧♦ Tfilo✳

■♥♦❧tr❡ ❞❛❧ ♣r♦❞♦tt♦ ∆V ·I s✐ ♦tt✐❡♥❡ ✐❧ ❝❛❧♦r❡ ❞✐ss✐♣❛t♦ ♣❡r ❡✛❡tt♦ ❏♦✉❧❡ ♥❡❧❧✬✉♥✐tà ❞✐ t❡♠♣♦

❡ ❞❛❧❧❡ r❡❧❛③✐♦♥✐ s✉❧❧♦ s❝❛♠❜✐♦ t❡r♠✐❝♦ s✐ ❤❛ ❝❤❡✿

PJoule = ∆V · I = Q̇ = h · Sfilo ·∆T ✭✸✳✻✮

❞♦✈❡ Sfilo è ❧❛ s✉♣❡r✜❝✐❡ ❞❡❧ ✜❧♦✱ ∆T è ❧❛ ❞✐✛❡r❡♥③❛ ❞✐ t❡♠♣❡r❛t✉r❛ tr❛ ✐❧ ✜❧♦ ❡❞ ✐❧ ✢✉✐❞♦

❛❞ ✉♥❛ s✉✣❝✐❡♥t❡ ❞✐st❛♥③❛✱ ♠❡♥tr❡ h è ✐❧ ❝♦❡✣❝✐❡♥t❡ ❞✐ ❝♦♥✈❡③✐♦♥❡ ❡❞ è ❧✬✉♥✐❝♦ t❡r♠✐♥❡

✐♥❝♦❣♥✐t♦ ❞❡❧❧✬❡q✉❛③✐♦♥❡✳ ■❧ ❝♦❡✣❝✐❡♥t❡ ❞✐ ❝♦♥✈❡③✐♦♥❡ h è ❢✉♥③✐♦♥❡ ❞✐ ❞✐✈❡rs✐ ♣❛r❛♠❡tr✐ tr❛

❝✉✐ ❧❛ ✈❡❧♦❝✐tà ❞❡❧ ✢✉✐❞♦ Va✳ ❈♦♥ ❧✬❛✉s✐❧✐♦ ❞✐ ♦♣♣♦rt✉♥❡ t❛❜❡❧❧❡ ❞✐ t❛r❛t✉r❛ ♠❡♠♦r✐③③❛t❡

♥❡❣❧✐ str✉♠❡t✐ ❡❧❡ttr♦♥✐❝✐ ❞✐ ❛❝q✉✐s✐③✐♦♥❡ è ♣♦ss✐❜✐❧❡ r✐s❛❧✐r❡ ❞✐r❡tt❛♠❡♥t❡ ❛❧ ✈❛❧♦r❡ ❞❡❧❧❛

✈❡❧♦❝✐tà ❞❡❧ ✢✉✐❞♦ Va ✐♥ m/s✳

❋✐❣✉r❛ ✸✳✸✿ ❆♥❡♠♦♠❡tr♦ ❛ ✜❧♦ ❝❛❧❞♦ ♦♠♥✐❞✐r❡③✐♦♥❛❧❡ ❉❡❧t❛❖❍▼ ❆P✸✷✵✸

✹✻

✸✳✹ ▼✐s✉r❛ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡

❉✐ s❡❣✉✐t♦ s✐ ❞❡s❝r✐✈❡ ✐❧ ♠❡t♦❞♦ ♣❡r ❞❡t❡r♠✐♥❛r❡ ❧❛ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡ ❛t✲

tr❛✈❡rs♦ ♠✐s✉r❛③✐♦♥❡ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ❞✐ ❣❧♦❜♦t❡r♠♦♠❡tr♦✱ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧❧✬❛r✐❛ ❡

❞❡❧❧❛ ✈❡❧♦❝✐tà ❞❡❧❧✬❛r✐❛✳

■❧ ❣❧♦❜♦t❡r♠♦♠❡tr♦ ❝♦♥st❛ ❞✐ ✉♥❛ s❢❡r❛ ❞✐ r❛♠❡ r✐❝♦♣❡rt❛ ❞✐ ✈❡r♥✐❝❡ ♥❡r❛ ♦♣❛❝❛ ❛❧ ❝❡♥tr♦

❞❡❧❧❛ q✉❛❧❡ è ♣♦st♦ ✉♥ s❡♥s♦r❡ ❞✐ t❡♠♣❡r❛t✉r❛ ✭t❡r♠♦❝♦♣♣✐❛ ♦ s❡♥s♦r❡ ❛ r❡s✐st❡♥③❛✮✳ ❙✐ ♣✉ò

✐♠♣✐❡❣❛r❡✱ t❡♦r✐❝❛♠❡♥t❡✱ ✉♥ ❣❧♦❜♦ ❝♦♥ ❞✐❛♠❡tr♦ q✉❛❧s✐❛s✐✱ t✉tt❛✈✐❛ ♥❡❧❧❛ ♥♦r♠❛ ❊◆ ■❙❖

✼✼✷✻ ❬✷✸❪ s✐ r❛❝❝♦♠❛♥❞❛ ✉♥ ❞✐❛♠❡tr♦ ❞✐ 0.15 m✳ ■♥❢❛tt✐ ♣❡r ❞✐❛♠❡tr✐ ♣✐ù ♣✐❝❝♦❧✐ s✐ ❤❛ ✉♥

♠❛❣❣✐♦r❡ ❡✛❡tt♦ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ❡ ❞❡❧❧❛ ✈❡❧♦❝✐tà ❞❡❧❧✬❛r✐❛✱ ✐❧ ❝❤❡ ♣r♦✈♦❝❛ ✉♥❛ r✐❞✉③✐♦♥❡

❞❡❧❧✬❛❝❝✉r❛t❡③③❛ ❞❡❧❧❛ ♠✐s✉r❛③✐♦♥❡ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡✳

■❧ ❣❧♦❜♦t❡r♠♦♠❡tr♦✱ ♣♦st♦ ♥❡❧❧✬❛♠❜✐❡♥t❡ ✐♥ ❝✉✐ s✐ ✈✉♦❧❡ ♠✐s✉r❛r❡ ❧❛ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛

r❛❞✐❛♥t❡ Tmr✱ t❡♥❞❡ ❛ ♣♦rt❛rs✐ ✐♥ ❝♦♥❞✐③✐♦♥✐ ❞✐ ❡q✉✐❧✐❜r✐♦ t❡r♠✐❝♦ ♣❡r ❡✛❡tt♦ ❞❡❣❧✐ s❝❛♠❜✐

❞♦✈✉t✐ ❛❧❧❛ r❛❞✐❛③✐♦♥❡ ♣r♦✈❡♥✐❡♥t❡ ❞❡❧❧❡ ❞✐✈❡rs❡ s♦r❣❡♥t✐ ❞✐ ❝❛❧♦r❡ ❞❡❧❧✬❛♠❜✐❡♥t❡ ❝✐r❝♦st❛♥t❡

❡ s♦tt♦ ❧✬❡✛❡tt♦ ❞❡❧❧♦ s❝❛♠❜✐♦ t❡r♠✐❝♦ ♣❡r ❝♦♥✈❡③✐♦♥❡✳ ▲❛ t❡♠♣❡r❛t✉r❛ ❞✐ ❣❧♦❜♦ r✐❧❡✈❛t❛✱

✐♥ ❝♦♥❞✐③✐♦♥✐ ❞✐ ❡q✉✐❧✐❜r✐♦ t❡r♠✐❝♦✱ ❞❛❧ s❡♥s♦r❡ ❞✐ t❡♠♣❡r❛t✉r❛ ♣♦st♦ ❛❧❧✬✐♥t❡r♥♦ ♣❡r♠❡tt❡

❞✐ ❞❡t❡r♠✐♥❛r❡ Tmr✳

▲✬❡q✉❛③✐♦♥❡ ❞✐ ❜✐❧❛♥❝✐♦ ❞❡❧❧✬❡♥❡r❣✐❛ tr❛ ✐❧ ❣❧♦❜♦t❡r♠♦♠❡tr♦ ❡ ❧✬❛♠❜✐❡♥t❡ ❝✐r❝♦st❛♥t❡ è

❡s♣r✐♠❜✐❜✐❧❡ ❝♦♠❡✿

qr + qc = 0 ✭✸✳✼✮

❞♦✈❡ qr è ✐❧ t❡r♠✐♥❡ ❞✐ s❝❛♠❜✐♦ t❡r♠✐❝♦ ♣❡r ✐rr❛❣❣✐❛♠❡♥t♦ ❡ qc r❛♣♣r❡s❡♥t❛ ❧♦ s❝❛♠❜✐♦ ❞✐

❝❛❧♦r❡ ♣❡r ❝♦♥✈❡③✐♦♥❡✳

✹✼

▲♦ s❝❛♠❜✐♦ t❡r♠✐❝♦ ♣❡r ✐rr❛❣❣✐❛♠❡♥t♦ è ❢✉♥③✐♦♥❡ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡ Tmr✿

qr = εgσ(

T 4

mr − T 4

g

)

✭✸✳✽✮

❞♦✈❡✿

εg è ❧✬❡♠✐ss✐✈✐tà ❞❡❧ ❣❧♦❜♦❀

σ è ❧❛ ❝♦st❛♥t❡ ❞✐ ❙t❡❢❛♥✲❇♦❧t③♠❛♥♥ ✭σ = 5, 67 · 10−8W/m2K4✮ ❀

Tmr è ❧❛ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡❀

Tg è ❧❛ t❡♠♣❡r❛t✉r❛ ❞✐ ❣❧♦❜♦✳

■❧ tr❛s❢❡r✐♠❡♥t♦ ❞✐ ❝❛❧♦r❡ ♣❡r ❝♦♥✈❡③✐♦♥❡ è ❡s♣r✐♠✐❜✐❧❡ ❝♦♠❡✿

qc = hcg (Ta − Tg) ✭✸✳✾✮

❞♦✈❡ hcg è ✐❧ ❝♦❡✣❝✐❡♥t❡ ❞✐ ❝♦♥✈❡③✐♦♥❡ ❛ ❧✐✈❡❧❧♦ ❞❡❧ ❣❧♦❜♦ ❝❤❡✱ ✐♥ ❝❛s♦ ❞✐ ❝♦♥✈❡③✐♦♥❡ ♥❛t✉r❛❧❡✱

❛ss✉♠❡ ❧✬❡s♣r❡ss✐♦♥❡✿

hcg = 1.4

(

∆T

D

)1/4

✭✸✳✶✵✮

♠❡♥tr❡ ✐♥ ❝❛s♦ ❞✐ ❝♦♥✈❡③✐♦♥❡ ❢♦r③❛t❛✿

hcg = 6.3V 0.6a

D0.4✭✸✳✶✶✮

❞♦✈❡ D è ✐❧ ❞✐❛♠❡tr♦ ❞❡❧ ❣❧♦❜♦ ❡ Va è ❧❛ ✈❡❧♦❝✐tà ❞❡❧❧✬❛r✐❛ ❛ ❧✐✈❡❧❧♦ ❞❡❧ ❣❧♦❜♦✳

❙♦st✐t✉❡♥❞♦ ❧❛ ✭✸✳✽✮ ❡ ❧❛ ✭✸✳✾✮ ♥❡❧❧❛ ✭✸✳✼✮ s✐ ❤❛ ✿

εgσ(

T 4

mr − T 4

g

)

+ hcg (Ta − Tg) = 0 ✭✸✳✶✷✮

❞❛ ❝✉✐✿

Tmr = 4

√

T 4g +

hcg

εgσ(Tg − Ta) ✭✸✳✶✸✮

◆❡❧ ❝❛s♦ ❞✐ ❝♦♥✈❡③✐♦♥❡ ♥❛t✉r❛❧❡ s✐ ♦tt✐❡♥❡✿

tmr =

[

(tg + 273)4 +0.25 · 108

εg

(

|tg − ta|

D

)1/4

(tg − ta)

]1/4

− 273 ✭✸✳✶✹✮

✹✽

◆❡❧ ❝❛s♦ ❞✐ ❣❧♦❜♦ st❛♥❞❛r❞ ❝♦♥ D = 0.15 m ❡ εg = 0.95 ✭♥❡r♦ ♦♣❛❝♦✮✱ ❧✬❡q✉❛③✐♦♥❡ ❛♣♣❡♥❛

♦tt❡♥✉t❛ ❞✐✈❡♥t❛✿

tmr =[

(tg + 273)4 + 0.4 · 108 |tg − ta|1/4 (tg − ta)

]1/4

− 273 ✭✸✳✶✺✮

◆❡❧ ❝❛s♦ ❞✐ ❝♦♥✈❡③✐♦♥❡ ❢♦r③❛t❛ s✐ ♦tt✐❡♥❡✿

tmr =

[

(tg + 273)4 +1.1 · 108V 0.6

a

εgD0.4(tg − ta)

]1/4

− 273 ✭✸✳✶✻✮

♣❡r ✐❧ ❣❧♦❜♦ st❛♥❞❛r❞ s✐ ❤❛✿

tmr =[

(tg + 273)4 + 2.5 · 108V 0.6a (tg − ta)

]1/4− 273 ✭✸✳✶✼✮

◗✉❡st✬✉❧t✐♠❛ è ❧✬❡s♣r❡ss✐♦♥❡ ♣✐ù ❢r❡q✉❡♥t❡♠❡♥t❡ ✉s❛t❛ ♣❡r ❝❛❧❝♦❧❛r❡ ❧❛ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛

r❛❞✐❛♥t❡ tmr✳ ❊ss❛ è ✈❛❧✐❞❛ s♦❧♦ ♣❡r ✐❧ ❣❧♦❜♦t❡r♠♦♠❡tr♦ st❛♥❞❛r❞ ❡❞ ✐♥ ❝♦♥❞✐③✐♦♥✐ ❞✐

❝♦♥✈❡③✐♦♥❡ ❢♦r③❛t❛✳

■♥ ❋✐❣✉r❛ ✸✳✹ s✐ ♠♦str❛ ❧✬✐♥✢✉❡♥③❛ r❡❧❛t✐✈❛ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧❧✬❛r✐❛ s✉❧❧❛ t❡♠♣❡r❛t✉r❛

❞✐ ❣❧♦❜♦ tg ✐♥ ❢✉♥③✐♦♥❡ ❞❡❧❧❛ ✈❡❧♦❝✐tà ❞❡❧❧✬❛r✐❛ ❡ ❞❡❧ ❞✐❛♠❡tr♦ ❞❡❧ ❣❧♦❜♦✳

❋✐❣✉r❛ ✸✳✹✿ ■♥✢✉❡♥③❛ r❡❧❛t✐✈❛ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧❧✬❛r✐❛ s✉❧❧❛ t❡♠♣❡r❛t✉r❛ ❞✐ ❣❧♦❜♦ tg ✐♥❢✉♥③✐♦♥❡ ❞❡❧❧❛ ✈❡❧♦❝✐tà ❞❡❧❧✬❛r✐❛ ❡ ❞❡❧ ❞✐❛♠❡tr♦ ❞❡❧ ❣❧♦❜♦ ✭❞❛ ❊◆ ■❙❖ ✼✼✷✻✱ ❊r❣♦♥♦♠✐❝s ♦❢t❤❡ t❤❡r♠❛❧ ❡♥✈✐r♦♥♠❡♥t ✐♥str✉♠❡♥ts ❢♦r ♠❡❛s✉r✐♥❣ ♣❤②s✐❝❛❧ q✉❛♥t✐t✐❡s✱ ✷✵✵✶✮

✹✾

❉❛❧ ♠♦♠❡♥t♦ ❝❤❡ ✉♥♦ ❞❡✐ ♣✐ù ✐♠♣♦rt❛♥t✐ ❢❛tt♦r✐ ❝❤❡ ❝♦♥❝♦rr♦♥♦ ❛❧❧❛ ❝❛r❛tt❡r✐③③❛③✐♦♥❡ ❞✐

✉♥ ❛♠❜✐❡♥t❡ ❞❛❧ ♣✉♥t♦ ❞✐ ✈✐st❛ t❡r♠✐❝♦ è ❧❛ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡✱ ✉♥❛ st✐♠❛ ❡rr❛t❛

❞✐ q✉❡st✬✉❧t✐♠❛ ♣✉ò ❝♦♥❞✉rr❡ ❛ ❣r❛♥❞✐ ❡rr♦r✐ ♥❡❧❧❛ ✈❛❧✉t❛③✐♦♥❡ ❝♦♠♣❧❡ss✐✈❛ ❞❡❧ ❝♦♠❢♦rt

t❡r♠✐❝♦✳ ❙✐ ❞♦✈r❡❜❜❡r♦ ❝♦♥s✐❞❡r❛r❡✱ q✉✐♥❞✐✱ ❧❡ s❡❣✉❡♥t✐ ♣r❡❝❛✉③✐♦♥✐ tr❛tt❡ ❞❛❧❧❛ ♥♦r♠❛ ❊◆

■❙❖ ✼✼✷✻✿

• ■♥ ❝❛s♦ ❞✐ r❛❞✐❛③✐♦♥❡ ❢♦rt❡♠❡♥t❡ ❡t❡r♦❣❡♥❡❛ è ♥❡❝❡ss❛r✐♦ ✉s❛r❡ tr❡ ❣❧♦❜♦t❡r♠♦♠❡tr✐✳

■♥❢❛tt✐ q✉❛♥❞♦ ❧❛ r❛❞✐❛③✐♦♥❡ è ❡t❡r♦❣❡♥❡❛ ❧❛ ♠✐s✉r❛③✐♦♥❡ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ❞✐ ❣❧♦✲

❜♦t❡r♠♦♠❡tr♦ ❡s❡❣✉✐t❛ ✐♥ ✉♥ s♦❧♦ ♣✉♥t♦ ♥♦♥ è r❛♣♣r❡s❡♥t❛t✐✈❛ ❞❡❧ ❝❛♠♣♦ r❛❞✐❛t✐✈♦

❝♦♠♣❧❡ss✐✈♦ r✐❝❡✈✉t♦ ❞❛❧ s♦❣❣❡tt♦✳ ❊✬✱ ❞✉♥q✉❡✱ ♥❡❝❡ss❛r✐♦ ♣♦rr❡ ✐ tr❡ ❣❧♦❜♦t❡r♠♦♠❡✲

tr✐ ✉♥♦ ❛ ❧✐✈❡❧❧♦ ❞❡❧❧❛ t❡st❛✱ ✉♥♦ ❞❡❧❧✬❛❞❞♦♠❡ ❡ ✉♥♦ ❞❡❧❧❡ ❝❛✈✐❣❧✐❡ ❡ ❧❛ t❡♠♣❡r❛t✉r❛

♠❡❞✐❛ r❛❞✐❛♥t❡ s✐ r✐❝❛✈❛ ❞❛❧❧❛ ♠❡❞✐❛ ♣❡s❛t❛ s❡❝♦♥❞♦ ♦♣♣♦rt✉♥✐ ❝♦❡✣❝✐❡♥t✐✳

• ■❧ t❡♠♣♦ ❞✐ r✐s♣♦st❛ ❞✐ ✉♥ ❣❧♦❜♦t❡r♠♦♠❡tr♦ è ❞✐ ❝✐r❝❛ 20 ÷ 30 ♠✐♥✉t✐ ❛ s❡❝♦♥❞❛

❞❡❧❧❡ ❝❛r❛tt❡r✐st✐❝❤❡ ✜s✐❝❤❡ ❞❡❧ ❣❧♦❜♦ ❡ ❞❡❧❧❡ ❝♦♥❞✐③✐♦♥✐ ❛♠❜✐❡♥t❛❧✐✳ ❆ ❝❛✉s❛ ❞❡❧❧❛ s✉❛

❡❧❡✈❛t❛ ✐♥❡r③✐❛ t❡r♠✐❝❛✱ ✐❧ ❣❧♦❜♦t❡r♠♦♠❡tr♦ ♥♦♥ ♣✉ò ❡ss❡r❡ ✐♠♣✐❡❣❛t♦ ✐♥ ❛♠❜✐❡♥t✐ ✐♥

❝✉✐ ❧❡ ❝♦♥❞✐③✐♦♥✐ r❛❞✐❛t✐✈❡ ✈❛r✐❛♥♦ r❛♣✐❞❛♠❡♥t❡✳

• ▲✬✉s♦ ❞❡❧ ❣❧♦❜♦t❡r♠♦♠❡tr♦ ♣❡r ❧❛ ✈❛❧✉t❛③✐♦♥❡ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡ è

s♦❧♦ ✉♥✬❛♣♣r♦s✐♠❛③✐♦♥❡ ♣♦✐❝❤è ✈✐ è ✉♥❛ ♥♦t❡✈♦❧❡ ❞✐✛❡r❡♥③❛ tr❛ ❧❛ ❢♦r♠❛ ❞❡❧ ❣❧♦❜♦

❡ ❧❛ ❢♦r♠❛ ❞❡❧ ❝♦r♣♦ ✉♠❛♥♦✳ ■♥ ♣❛rt✐❝♦❧❛r❡✱ ❧❛ r❛❞✐❛③✐♦♥❡ ♣r♦✈❡♥✐❡♥t❡ ❞❛❧ s♦✣tt♦

❡ ❞❛❧ ♣❛✈✐♠❡♥t♦ r✐s✉❧t❡rà s♦✈r❛st✐♠❛t❛ ❞❛❧ ❣❧♦❜♦ r✐s♣❡tt♦ q✉❡❧❧❛ r✐❝❡✈✉t❛ ❞❛ ✉♥❛

♣❡rs♦♥❛ ✐♥ ♣✐❡❞✐ ♦ s❡❞✉t❛✳ ■♥ ❚❛❜❡❧❧❛ ✸✳✹ s✐ r✐♣♦rt❛♥♦ ✐ ❢❛tt♦r✐ ❞✬❛r❡❛ ♣r♦✐❡tt❛t✐ ♣❡r

✉♥❛ ♣❡rs♦♥❛✱ ✉♥✬❡❧✐ss♦✐❞❡ ❡❞ ✉♥❛ s❢❡r❛✳ ❙✐ ♦ss❡r✈❛ ❝❤❡ ❧✬❡❧✐ss♦✐❞❡ ❛♣♣r♦ss✐♠❛ ♠❡❣❧✐♦

❧❛ ❢♦r♠❛ ❞❡❧ ❝♦r♣♦ ✉♠❛♥♦ s✐❛ ✐♥ ♣♦s✐③✐♦♥❡ ✐♥ ♣✐❡❞✐ ❝❤❡ s❡❞✉t❛✳ ■❧ ❢❛tt♦r❡ ❞✬❛r❡❛

♣r♦✐❡tt❛t♦ ✐♥❞✐❝❛ ❧✬✐♠♣♦rt❛♥③❛ r❡❧❛t✐✈❛ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ ❞❛❧❧❡ s❡✐ ❞✐✛❡r❡♥t✐ ❞✐r❡③✐♦♥✐

❡❞ è ❞❛t♦ ❞❛❧ r❛♣♣♦rt♦ Apr/Ar ❞♦✈❡ Apr è ❧✬❛r❡❛ ❞❡❧❧❛ s✉♣❡r✜❝✐❡ ♣r♦✐❡tt❛t❛ ✐♥ ✉♥❛

❞✐r❡③✐♦♥❡ ❡❞ Ar è ❧✬❛r❡❛ t♦t❛❧❡ ❞❡❧❧❛ s✉♣❡r✜❝✐❡ r❛❞✐❛♥t❡✳

✺✵

• ■❧ ❣❧♦❜♦t❡r♠♦♠❡tr♦ ♥❡r♦ s♦✈r❛st✐♠❛ ❧✬✐♥✢✉❡♥③❛ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ ❛❞ ♦♥❞❛ ❝♦rt❛ ✭♣❡r

❡s❡♠♣✐♦ ❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡✮✱ ♣❡rt❛♥t♦ r✐s✉❧t❛ ♦♣♣♦rt✉♥♦ ✐♠♣✐❡❣❛r❡ ✉♥ ❣❧♦❜♦ r✐✲

❝♦♣❡rt♦ ❞✐ ✈❡r♥✐❝❡ ❞✐ ❝♦❧♦r❡ ❣r✐❣✐♦ ♦♣❛❝♦ ❝❤❡ ♠❡❣❧✐♦ ❛♣♣r♦ss✐♠❛ ❧❡ ❝❛r❛tt❡r✐s❝t✐❝❤❡

❡♥❡r❣❡t✐❝❤❡ ❞❡✐ ✈❡st✐t✐✳ ■♥ ❛❧t❡r♥❛t✐✈❛ è ♣♦ss✐❜✐❧❡ ✉s❛r❡ ✐❧ ❣❧♦❜♦t❡r♠♦♠❡tr♦ ♥❡r♦ ❡

❝❛❧❝♦❧❛r❡ ❧❛ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡ t❡♥❡♥❞♦ ❝♦♥t♦ ❞❡❧❧✬❛ss♦r❜✐♠❡♥t♦ ❞❡✐ ✈❡st✐t✐

✐♥❞♦ss❛t✐✳

❙♦♣r❛✴❙♦tt♦ ❙✐♥✐str❛✴❉❡str❛ ❆✈❛♥t✐✴❉✐❡tr♦

■♥ ♣✐❡❞✐P❡rs♦♥❛❊❧❧✐ss♦✐❞❡❙❢❡r❛

0.080.080.25

0.230.280.25

0.350.280.25

❙❡❞✉t♦P❡rs♦♥❛❊❧❧✐ss♦✐❞❡❙❢❡r❛

0.180.180.25

0.220.220.25

0.300.280.25

❚❛❜❡❧❧❛ ✸✳✹✿ ❋❛tt♦r✐ ❞✬❛r❡❛ ♣r♦✐❡tt❛t✐

✺✶

◆❡❧❧❛ ❝❛♠♣❛❣♥❛ ❞✐ ♠✐s✉r❡✱ ♣❡r r✐❧❡✈❛r❡ ❧✬❛♥❞❛♠❡♥t♦ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡

❛❧ ❞✐ s♦tt♦ ❞❡❧❧❛ ❝♦♣❡rt✉r❛✱ è st❛t❛ ✐♠♣✐❡❣❛t❛ ❧❛ s♦♥❞❛ ❣❧♦❜♦t❡r♠♦♠❡tr♦ ♥❡r♦ st❛♥❞❛r❞

❉❡❧t❛❖❍▼ ❚P✸✷✼✺ ✭❋✐❣✉r❛ ✸✳✺ ✮ ❝♦❧❧❡❣❛t❛ ❛❧❧❛ ❝❡♥tr❛❧✐♥❛ ❞✐ ❛❝q✉✐s✐③✐♦♥❡ ❞❡✐ ♣❛r❛♠❡tr✐

♠✐❝r♦❝❧✐♠❛t✐❝✐ ❉❡❧t❛❖❍▼ ❍❉✸✷✳✶✳ ■❧ ❞❛t♦ ❛❝q✉✐s✐t♦ ❞✐ t❡♠♣❡r❛t✉r❛ ❞✐ ❣❧♦❜♦t❡r♠♦♠❡tr♦

tg ✉♥✐t❛♠❡♥t❡ ❛✐ ❞❛t✐ ❞✐ t❡♠♣❡r❛t✉r❛ ❞❡❧❧✬❛r✐❛ ta ❡ ✈❡❧♦❝✐tà ❞❡❧❧✬❛r✐❛ Va s♦♥♦ st❛t✐ ❝♦♠❜✐♥❛t✐

♥❡❧❧❛ ❢♦r♠✉❧❛ ✭✸✳✶✼✮ ♣❡r ✐❧ ❝❛❧❝♦❧♦ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡ tmr✳ ▲❡ ❝❛r❛tt❡r✐st✐❝❤❡

❞❡❧ ❣❧♦❜♦ ❡ ❧❡ s♣❡❝✐✜❝❤❡ ❞❡❧ s❡♥s♦r❡ ❞✐ t❡♠♣❡r❛t✉r❛ ✉t✐❧✐③③❛t♦ s♦♥♦ r✐♣♦rt❛t❡ ✐♥ ❚❛❜❡❧❧❛ ✸✳✺✳

❉✐❛♠❡tr♦ ❞✐ ❣❧♦❜♦ φ = 150 mm

❚✐♣♦ s❡♥s♦r❡ Pt✶✵✵

❘❛♥❣❡ ❞✐ ♠✐s✉r❛ −10÷+100◦❈

■♥❝❡rt❡③③❛ ❞✐ ♠✐s✉r❛ ❈❧❛ss❡ 1/3 ❉■◆

❚❡♠♣♦ ❞✐ r✐s♣♦st❛ T95 15′

❚❛❜❡❧❧❛ ✸✳✺✿ ❙♣❡❝✐✜❝❤❡ t❡❝♥✐❝❤❡ ❞❡❧❧❛ s♦♥❞❛ ❣❧♦❜♦t❡r♠♦♠❡tr♦ ❉❡❧t❛❖❍▼ ❚P✸✷✼✺

❋✐❣✉r❛ ✸✳✺✿ ❙♦♥❞❛ ❣❧♦❜♦t❡r♠♦♠❡tr♦ ❉❡❧t❛❖❍▼ ❚P✸✷✼✺

✺✷

✸✳✺ ▼✐s✉r❛ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧❧❡ s✉♣❡r✜❝✐

❖❧tr❡ ❛✐ ♣❛r❛♠❡tr✐ ♠✐❝r♦❝❧✐♠❛t✐❝✐ r✐❧❡✈❛t✐ s♦tt♦ ❧❛ ❝♦♣❡rt✉r❛ q✉❛❧✐ ❧❛ t❡♠♣❡r❛t✉r❛

❞❡❧❧✬❛r✐❛✱ ❧✬✉♠✐❞✐tà r❡❧❛t✐✈❛✱ ❧❛ ✈❡❧♦❝✐tà ❞❡❧❧✬❛r✐❛ ❡ ❧❛ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡✱ ♣❡r ❧❛

✈❛❧✐❞❛③✐♦♥❡ ❞❡❧ ♠♦❞❡❧❧♦ ♥✉♠❡r✐❝♦✱ s✐ è r❡s❛ ♥❡❝❡ss❛r✐❛ ❧✬❛❝q✉✐s✐③✐♦♥❡ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧❧❛

s✉♣❡r✜❝✐❡ ✐♥t❡r♥❛ ❞❡❧❧❛ ❝♦♣❡rt✉r❛ ❡ ❞❡❧❧❛ s✉♣❡r✜❝✐❡ ❞❡❧ ♣❛✈✐♠❡♥t♦✳ P❡r q✉❡st♦ s❝♦♣♦ s♦♥♦

st❛t❡ ✐♠♣✐❡❣❛t❡ ❞✉❡ t❡r♠♦❝♦♣♣✐❡ ❝♦❧❧❡❣❛t❡ ❛❞ ✉♥ ♠✉❧t✐♠❡tr♦ ❞✐❣✐t❛❧❡ ♣❡r ❧✬❡❧❛❜♦r❛③✐♦♥❡ ❡

❧❛ ♠❡♠♦r✐③③❛③✐♦♥❡ ❞❡✐ ❞❛t✐✳

▲❡ t❡r♠♦❝♦♣♣✐❡ s♦♥♦ s❡♥s♦r✐ ❞✐ t❡♠♣❡r❛t✉r❛ ❧❛r❣❛♠❡♥t❡ ❞✐✛✉s✐ ❡❞ ❛♠♣✐❛♠❡♥t❡ ✉t✐❧✐③③❛t✐

♣❡r❝❤è ❡❝♦♥♦♠✐❝✐✱ st❛♥❞❛r❞✐③③❛t✐ ❡ ♣♦ss♦♥♦ ❧❛✈♦r❛r❡ s✉ ❛♠♣✐ ✐♥t❡r✈❛❧❧✐ ❞✐ t❡♠♣❡r❛t✉r❛✳ ■❧

❧♦r♦ ❢✉♥③✐♦♥❛♠❡♥t♦ è ❜❛s❛t♦ s✉ ✉♥ ❢❡♥♦♠❡♥♦ ♣❡r ✐❧ q✉❛❧❡✱ s❡ ❞✉❡ ❞✐✛❡r❡♥t✐ ♠❡t❛❧❧✐ s♦♥♦

✉♥✐t✐ ❛ss✐❡♠❡ ❛ ❢♦r♠❛r❡ ✉♥❛ ❣✐✉♥③✐♦♥❡✱ s✐ ✐♥st❛✉r❛ ✉♥❛ ❞✐✛❡r❡♥③❛ ❞✐ ♣♦t❡♥③✐❛❧❡ ❝❤❡ ❞✐♣❡♥❞❡

❞❛❧ t✐♣♦ ❞✐ ♠❡t❛❧❧✐ ✉s❛t✐ ❡ ❞❛❧❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧❧❛ ❣✐✉♥③✐♦♥❡✳ ◗✉✐♥❞✐ ✉♥❛ t❡r♠♦❝♦♣♣✐❛ è ✉♥

❝✐r❝✉✐t♦ ❝♦♠♣❧❡t♦ ❝❤❡ ✐♠♣❧✐❝❛ ❞✉❡ ❣✐✉♥③✐♦♥✐ tr❛ ❞✉❡ ❝♦♥❞✉tt♦r✐ ❞✐ ♥❛t✉r❛ ❞✐✈❡rs❛✱ ❋✐❣✉r❛

✸✳✻✿

❋✐❣✉r❛ ✸✳✻✿ ❚❡r♠♦❝♦♣♣✐❛ ✭❞❛ ❲✳ ❇♦❧t♦♥✱ ▼❡❝❤❛tr♦♥✐❝s ✲❊❧❡❝tr♦♥✐❝ ❝♦♥tr♦❧ s②st❡♠s ✐♥♠❡❝❤❛♥✐❝❛❧ ❡♥❣✐♥❡❡r✐♥❣✱ ❆❞❞✐s♦♥ ❲❡s❧❡② ▲♦♥❣♠❛♥✱ ◆❡✇ ❨♦r❦ ✶✾✾✾✮

❙❡ ❡♥tr❛♠❜❡ ❧❡ ❣✐✉♥③✐♦♥✐ s✐ tr♦✈❛♥♦ ❛❧❧❛ st❡ss❛ t❡♠♣❡r❛t✉r❛ ♥♦♥ s✐ ♠❛♥✐❢❡st❛ ❛❧❝✉♥❛ ❢♦r③❛

❡❧❡ttr♦♠♦tr✐❝❡✱ s❡ ❛❧ ❝♦♥tr❛r✐♦ ✈✐ è ✉♥❛ ❞✐✛❡r❡♥③❛ ❞✐ t❡♠♣❡r❛t✉r❛✱ s✐ ✐♥st❛✉r❛ ✉♥❛ ❢✳❡✳♠✳

♥♦♥ ♥✉❧❧❛ ❛✐ ❝❛♣✐ ❞❡❧ ❝✐r❝✉✐t♦✳ ■❧ ✈❛❧♦r❡ ❛ss♦❧✉t♦ ❞ q✉❡st❛ ❢✳❡✳♠✳ ❞✐♣❡♥❞❡ ❞❛❧❧❛ ♥❛t✉r❛

❞❡✐ ❞✉❡ ♠❡t❛❧❧✐ ✐♥t❡r❡ss❛t✐ ❡ ❞❛❧❧❡ t❡♠♣❡r❛t✉r❡ ❞✐ ❡♥tr❛♠❜❡ ❧❡ ❣✐✉♥③✐♦♥✐✳ ❙♦❧✐t❛♠❡♥t❡ ✉♥❛

❣✐✉♥③✐♦♥❡✱ ❞❡tt❛ ❣✐✉♥③✐♦♥❡ ❞✐ r✐❢❡r✐♠❡♥t♦✱ è ♠❛♥t❡♥✉t❛ ❛ 0◦C ❡ ✈❛❧❡ ❧❛ s❡❣✉❡♥t❡ r❡❧❛③✐♦♥❡

q✉❛❞r❛t✐❝❛ ✭❧✐♥❡❛r✐③③❛❜✐❧❡ ❧✐♠✐t❛♥❞♦ ❧✬✐♥t❡r✈❛❧❧♦ ❞✐ t❡♠♣❡r❛t✉r❛✮✿

✺✸

E = at+ bt2 ✭✸✳✶✽✮

❞♦✈❡ a ❡ b s♦♥♦ ❝♦st❛♥t✐ ♣❡r ✐ ♠❡t❛❧❧✐ ✉s❛t✐✳

❙♦♥♦ ❞✐ ✉s♦ ❝♦♠✉♥❡ ❧❡ t❡r♠♦❝♦♣♣✐❡ ♠♦str❛t❡ ✐♥ ❚❛❜❡❧❧❛ ✸✳✻✱ ❞♦✈❡ s♦♥♦ r✐♣♦rt❛t❡ ❧❛ ❧❡t✲

t❡r❛ ❞✐ r✐❢❡r✐♠❡♥t♦✱ ✐ ♠❛t❡r✐❛❧✐ ✐♠♣✐❡❣❛t✐ ♥❡❧❧❛ ❣✐✉♥③✐♦♥❡✱ ❧✬✐♥t❡r✈❛❧❧♦ ❞✐ t❡♠♣❡r❛t✉r❛ ❞✐

❢✉♥③✐♦♥❛♠❡♥t♦ ❡ ❧❛ s❡♥s✐❜✐❧tà✳

❘✐❢❡r✐♠❡♥t♦ ▼❛t❡r✐❛❧✐ ■♥t❡r✈❛❧❧♦ ◦❈ ❙❡♥s✐❜✐❧✐tà µV/◦❈

❇ P❧❛t✐♥♦ 30% ❘♦❞✐♦✴P❧❛t✐♥♦ 6% ❘♦❞✐♦ 0÷ 1800 3

❊ ❈❤r♦♠❡❧✴❈♦st❛♥t❛♥❛ −200÷ 900 63

❏ ❋❡rr♦✴❈♦st❛♥t❛♥❛ −200÷ 900 53

❑ ❈❤r♦♠❡❧✴❆❧✉♠❡❧ −200÷ 1300 41

◆ ◆✐❝r♦s✐❧✴◆✐s✐❧ −200÷ 1300 28

❘ P❧❛t✐♥♦✴P❧❛t✐♥♦ 13% ❘♦❞✐♦ 0÷ 1400 6

❙ P❧❛t✐♥♦✴P❧❛t✐♥♦ 10% ❘♦❞✐♦ 0÷ 1400 6

❚ ❘❛♠❡✴❈♦st❛♥t❛♥❛ −200÷ 400 43

❚❛❜❡❧❧❛ ✸✳✻✿ ❚✐♣✐ ❞✐ t❡r♠♦❝♦♣♣✐❡ ✭❞❛ ❲✳ ❇♦❧t♦♥✱ ▼❡❝❤❛tr♦♥✐❝s ✲❊❧❡❝tr♦♥✐❝ ❝♦♥tr♦❧ s②st❡♠s✐♥ ♠❡❝❤❛♥✐❝❛❧ ❡♥❣✐♥❡❡r✐♥❣✱ ❆❞❞✐s♦♥ ❲❡s❧❡② ▲♦♥❣♠❛♥✱ ◆❡✇ ❨♦r❦ ✶✾✾✾✮

■♥ ❋✐❣✉r❛ ✸✳✼ s✐ ♠♦str❛✱ ♣❡r ❛❧❝✉♥❡ t✐♣♦❧♦❣✐❡ ❞✐ t❡r♠♦❝♦♣♣✐❡✱ ❧✬❛♥❞❛♠❡♥t♦ ❞❡❧❧❛ ❢✳❡✳♠✳ ❛❧

✈❛r✐❛r❡ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ❛❧❧❛ q✉❛❧❡ s✐ tr♦✈❛ ❧❛ ❣✐✉♥③✐♦♥❡ ❝❛❧❞❛✳

P❡r ❧❛ ▲❡❣❣❡ ❞❡✐ ♠❡t❛❧❧✐ ✐♥t❡r♠❡❞✐ è ♣♦ss✐❜✐❧❡ ❞✐♠♦str❛r❡ ❝❤❡✱ ❧❛ ♣r❡s❡♥③❛ ❞✐ ❡✈❡♥t✉❛❧✐

❝❛✈✐ ❝♦♥❞✉tt♦r✐ ❞✐ ♥❛t✉r❛ ❞✐✈❡rs❛ r✐s♣❡tt♦ ❛✐ ❞✉❡ ♠❡t❛❧❧✐ ❝❤❡ r❡❛❧✐③③❛♥♦ ❧❛ ❣✐✉♥③✐♦♥❡✱ ♥♦♥

✐♥✢✉✐s❝❡ s✉❧❧❛ ❢✳❡✳♠✳ ❣❡♥❡r❛t❛✱ ✐♥❢❛tt✐ s❡ ❧❡ ❞✉❡ ❣✐✉♥③✐♦♥✐ tr❛ ▼❡t❛❧❧♦ ❆ ❡ ❝❛✈✐ s✐ tr♦✈❛♥♦

❛❧❧❛ st❡ss❛ t❡♠♣❡r❛t✉r❛ ❣❡♥❡r❛♥♦ ❞✉❡ ❢✳❡✳♠✳ ✉❣✉❛❧✐ ✐♥ ✈❛❧♦r❡ ❛ss♦❧✉t♦ ♠❛ ❞✐ s❡❣♥♦ ♦♣♣♦st♦

t❛❧✐ ❝❤❡✱ ❛♣♣❧✐❝❛♥❞♦ ❧❛ ▲❡❣❣❡ ❞✐ ❑✐r❝❤❤♦✛ ❞❡❧❧❡ t❡♥s✐♦♥✐ ❛❧ ❝✐r❝✉✐t♦✱ s✐ ❡❧✐❞♦♥♦✳

❯♥❛ t❡r♠♦❝♦♣♣✐❛ ♣✉ò ❡ss❡r❡ ✉s❛t❛ ❝♦♥ ❧❛ ❣✐✉♥③✐♦♥❡ ❞✐ r✐❢❡r✐♠❡♥t♦ ❛❞ ✉♥❛ t❡♠♣❡r❛t✉r❛

s✉♣❡r✐♦r❡ ❛ ✵◦❈✳ ❚✉tt❛✈✐❛✱ ❞❛❧ ♠♦♠❡♥t♦ ❝❤❡ ❧❡ t❛❜❡❧❧❡ ❞✐ ❝♦♥✈❡rs✐♦♥❡ t❡♥s✐♦♥❡✲t❡♠♣❡r❛t✉r❛

✺✹

❋✐❣✉r❛ ✸✳✼✿ ❢✳❡✳♠✳ ✐♥ ❢✉♥③✐♦♥❡ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ♣❡r ❛❧❝✉♥❡ t✐♣♦❧♦❣✐❡ ❞✐ t❡r♠♦❝♦♣♣✐❡ ✭❞❛❲✳ ❇♦❧t♦♥✱ ▼❡❝❤❛tr♦♥✐❝s ✲❊❧❡❝tr♦♥✐❝ ❝♦♥tr♦❧ s②st❡♠s ✐♥ ♠❡❝❤❛♥✐❝❛❧ ❡♥❣✐♥❡❡r✐♥❣✱ ❆❞❞✐s♦♥❲❡s❧❡② ▲♦♥❣♠❛♥✱ ◆❡✇ ❨♦r❦ ✶✾✾✾✮

s♦♥♦ r❡❛❧✐③③❛t❡ ❛ss✉♠❡♥❞♦ ❧❛ ❣✐✉♥③✐♦♥❡ ❞✐ r✐❢❡r✐♠❡♥t♦ ❛ ✵◦❈✱ r✐s✉❧t❛ ♥❡❝❡ss❛r✐♦ ❛♣♣❧✐❝❛r❡

✉♥❛ ❝♦rr❡③✐♦♥❡ ❝❤❡ s❢r✉tt❛ ❧❛ ▲❡❣❣❡ ❞❡❧❧❡ t❡♠♣❡r❛t✉r❡ ✐♥t❡r♠❡❞✐❡✿

Et,0 = Et,I + EI,0 ✭✸✳✶✾✮

▲❛ ❢♦r③❛ ❡❧❡ttr♦♠♦tr✐❝❡ ❊t,0 ❣❡♥❡r❛t❛ ❞❛❧❧❛ ❣✐✉♥③✐♦♥❡ ❝❛❧❞❛ ❛❧❧❛ t❡♠♣❡r❛t✉r❛ t q✉❛♥❞♦ ❧❛

❣✐✉♥③✐♦♥❡ ❞✐ r✐❢❡r✐♠❡♥t♦ è ❛ ✵◦❈✱ ❡❣✉❛❣❧✐❛ ❧❛ ❢✳❡✳♠✳ Et,I ❣❡♥❡r❛t❛ ❞❛❧❧❛ ❣✐✉♥③✐♦♥❡ ❝❛❧❞❛ ❛❧❧❛

t❡♠♣❡r❛t✉r❛ t q✉❛♥❞♦ ❧❛ ❣✐✉♥③✐♦♥❡ ❞✐ r✐❢❡r✐♠❡♥t♦ è ❛ t❡♠♣❡r❛t✉r❛ ❛♠❜✐❡♥t❡ I ✭✈❛❧♦r❡ ❞✐

t❡♥s✐♦♥❡ ♠✐s✉r❛t♦✮ s♦♠♠❛t❛ ❛❧❧❛ ❢♦r③❛ ❡❧❡ttr♦♠♦tr✐❝❡ EI,0 ❣❡♥❡r❛t❛ ❞❛❧❧❛ ❣✐✉♥③✐♦♥❡ ❝❛❧❞❛

❛❧❧❛ t❡♠♣❡r❛t✉r❛ ❛♠❜✐❡♥t❡ I q✉❛♥❞♦ ❧❛ ❣✐✉♥③✐♦♥❡ ❞✐ r✐❢❡r✐♠❡♥t♦ è ❛ ✵◦❈✳ P❡r ❛♣♣❧✐❝❛r❡

q✉❡st❛ ❝♦rr❡③✐♦♥❡ s✐ ✐♠♣✐❡❣❛ ✉♥ ❝✐r❝✉✐t♦ ❞✐ ❝♦♠♣❡♥s❛③✐♦♥❡ ✭❋✐❣✉r❛ ✸✳✽ ✮ ✐❧ q✉❛❧❡✱ r✐❧❡✈❛t❛

❝♦♥ ✉♥ t❡r♠♦♠❡tr♦ ❛ r❡s✐st❡♥③❛ ❧❛ t❡r♠♣❡r❛t✉r❛ ❛♠❜✐❡♥t❡ I ❡ ❜❛s❛♥❞♦s✐ s✉ ✉♥❛ t❛❜❡❧❧❛

❞✐ ❧❡tt✉r❛ ♣r❡❝❛r✐❝❛t❛✱ ❣❡♥❡r❛ ❧❛ t❡♥s✐♦♥❡ EI,0 ❞❛ s♦♠♠❛r❡ ❛❧❧❛ t❡♥s✐♦♥❡ Et,I ♣❡r ♦tt❡♥❡r❡

❊t,0✳

✺✺

❋✐❣✉r❛ ✸✳✽✿ ❈✐r❝✉✐t♦ ❞✐ ❝♦♠♣❡♥s❛③✐♦♥❡ ✭❞❛ ❲✳ ❇♦❧t♦♥✱ ▼❡❝❤❛tr♦♥✐❝s ✲❊❧❡❝tr♦♥✐❝ ❝♦♥tr♦❧s②st❡♠s ✐♥ ♠❡❝❤❛♥✐❝❛❧ ❡♥❣✐♥❡❡r✐♥❣✱ ❆❞❞✐s♦♥ ❲❡s❧❡② ▲♦♥❣♠❛♥✱ ◆❡✇ ❨♦r❦ ✶✾✾✾✮

▲❡ t❡r♠♦❝♦♣♣✐❡ ✐♥ ♠❡t❛❧❧♦ ✈✐❧❡✱ ❝♦♠❡ ❊✱ ❏✱ ❑ ❡ ❚✱ s♦♥♦ ❛❜❜❛st❛♥③❛ ❡❝♦♥♦♠✐❝❤❡✱ ♠❛ t❡♥❞♦♥♦

❛ ❞❡❣r❛❞❛r❡ ♥❡❧ t❡♠♣♦ ❡❞ ❤❛♥♥♦ ✉♥✬❛❝❝✉r❛t❡③③❛±1÷3%✳ ▲❡ t❡r♠♦❝♦♣♣✐❡ ✐♥ ♠❡t❛❧❧♦ ♥♦❜✐❧❡✱

❝♦♠❡ ❘✱ s♦♥♦ ♣✐ù ❝♦st♦s❡✱ ♠❛ s♦♥♦ ♣✐ù st❛❜✐❧✐ ♥❡❧ t❡♠♣♦ ❡❞ ❤❛♥♥♦ ✉♥✬❛❝❝✉r❛t❡③③❛ ♠✐♥♦r❡

❞✐ ±1✪✳

◆❡❧❧❛ ❝❛♠♣❛❣♥❛ ❞✐ ♠✐s✉r❡ s♣❡r✐♠❡♥t❛❧✐ s✐ s♦♥♦ ♠❡ss❡ ✐♥ ♦♣❡r❛ ❞✉❡ t❡r♠♦❝♦♣♣✐❡ t✐♣♦ ❏✿

✉♥❛ t❡r♠♦❝♦♣♣✐❛ ✜ss❛t❛ ❛❧❧❛ ❝♦♣❡rt✉r❛ ✐♥ ✈❡tr♦ ❧❛t♦ ✐♥t❡r♥♦ ❝♦♥ ♥❛str♦ ❛❞❡s✐✈♦ tr❛s♣❛r❡♥t❡

✭❋✐❣✉r❛ ✸✳✾ ❛✮✱ ❧✬❛❧tr❛ ❛ ❝♦♥t❛tt♦ ❝♦♥ ❧❛ s✉♣❡r✜❝✐❡ ❞❡❧ ♣❛✈✐♠❡♥t♦ ✐♥ ♣♦r✜❞♦ ❛❧ ❞✐ s♦tt♦ ❞❡❧❧❛

❝♦♣❡rt✉r❛ ✭❋✐❣✉r❛ ✸✳✾ ❜✮

✭❛✮ ✭❜✮

❋✐❣✉r❛ ✸✳✾✿ ▼❡ss❛ ✐♥ ♦♣❡r❛ ❞❡❧❧❡ t❡r♠♦❝♦♣♣✐❡ ♥❡❧❧❛ ❝❛♠♣❛❣♥❛ ❞✐ ♠✐s✉r❡

✺✻

✸✳✻ ▼✐s✉r❛ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡

❉✐ s❡❣✉✐t♦ ✈❡♥❣♦♥♦ ❞❡s❝r✐tt✐ ❣❧✐ str✉♠❡♥t✐ ✉t✐❧✐③③❛t✐ ♥❡❧❧❛ ❝❛♠♣❛❣♥❛ ❞✐ ♠✐s✉r❡ ♣❡r

r✐❧❡✈❛r❡ ❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ s♦tt♦ ❡ ❢✉♦r✐ ❧❛ ❝♦♣❡rt✉r❛✳

■♥ ❋✐❣✉r❛ ✸✳✶✵ s✐ ♠♦str❛♥♦ s❝❤❡♠❛t✐❝❛♠❡♥t❡ ✐ ✢✉ss✐ ❞✐ r❛❞✐❛③✐♦♥❡ ♣r✐♠❛r✐❛ s✉ ✉♥❛ s✉♣❡r✜❝✐❡

s✉❞❞✐✈✐s✐ ✐♥ ❞✉❡ r❛♥❣❡ ❞✐ ❧✉♥❣❤❡③③❛ ❞✬♦♥❞❛✿

✶✳ Radiazione solare ♦ a bassa lunghezza d′onda✿ è ❧❛ r❛❞✐❛③✐♦♥❡ ♣r♦✈❡♥✐❡♥t❡ ❞❛❧ ❙♦❧❡✱

✉♥❛ s♦r❣❡♥t❡ ❛ t❡♠♣❡r❛t✉r❛ ♣r♦ss✐♠❛ ❛ 6000 K✱ ❝♦♥ ❧✉♥❣❤❡③③❛ ❞✬♦♥❞❛ ❝♦♠♣r❡s❛ tr❛

0.3 ❡ 3 µm ✳

✷✳ Radiazione a grande lunghezza d′onda✿ è ❧❛ r❛❞✐❛③✐♦♥❡ ❡♠❡ss❛ ❞❛ s♦r❣❡♥t✐ ❝❤❡

❤❛♥♥♦ t❡♠♣❡r❛t✉r❛ ♣r♦ss✐♠❛ ❛❧❧❛ t❡♠♣❡r❛t✉r❛ ❛♠❜✐❡♥t❡ ❡ ❝❤❡ ❤❛ q✉✐♥❞✐ ❧✉♥❣❤❡③③❛

❞✬♦♥❞❛ ♠❛❣❣✐♦r❡ ❞✐ 3 µm.

❋✐❣✉r❛ ✸✳✶✵✿ ❘❛❞✐❛③✐♦♥❡ s✉ ✉♥❛ s✉♣❡r✜❝✐❡

❊s✐st♦♥♦ ❞✉❡ t✐♣♦❧♦❣✐❡ ❞✐ str✉♠❡♥t✐ ♣❡r ♠✐s✉r❛r❡ ❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡✿

Piranometro✿ str✉♠❡♥t♦ ♣❡r ♠✐s✉r❛r❡ ❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ t♦t❛❧❡ ❡♠✐s❢❡r✐❝❛ ✭❞✐r❡tt❛ ❡

❞✐✛✉s❛✮ r❛♣♣r❡s❡♥t❛t❛ ❞❛ ✉♥❛ ❡♥❡r❣✐❛ ♣❡r ✉♥✐tà ❞✐ t❡♠♣♦ ♣❡r ✉♥✐tà ❞✐ ❛r❡❛ ❝♦♥ s✉♣❡r✜❝✐❡

❞✐ r❛❝❝♦❧t❛ ♦r✐③③♦♥t❛❧❡✳ ◗✉❛❧♦r❛ ✐❧ r✐❧❡✈❛t♦r❡ ✈❡♥❣❛ s❝❤❡r♠❛t♦ ❞❛❧❧❛ r❛❞✐❛③✐♦♥❡ ❞✐r❡tt❛

♠❡❞✐❛♥t❡ ✉♥ ❛♥❡❧❧♦ ♦♣❛❝♦ ♦ ✉♥ ❞✐s❝♦✱ ❧♦ str✉♠❡♥t♦ ♠✐s✉r❛ s♦❧❛ ❧❛ r❛❞✐❛③✐♦♥❡ ❞✐✛✉s❛❀

✺✼

Pireliometro✿ str✉♠❡♥t♦ ❝❤❡ ✉s❛ ✉♥ r✐❧❡✈❛t♦r❡ ♣❡r ♠✐s✉r❛r❡ ❧❛ r❛❞✐❛③✐♦♥❡ ♣r♦✈❡♥✐❡♥t❡

❞❛ ✉♥❛ ♣✐❝❝♦❧❛ ♣♦r③✐♦♥❡ ❞✐ ❝✐❡❧♦ ❝♦♠♣r❡♥❞❡♥t❡ ✐❧ ❙♦❧❡ ✭r❛❞✐❛③✐♦♥❡ ❞✐r❡tt❛✮ ❡❞ ✐♥❝✐❞❡♥t❡

♥♦r♠❛❧♠❡♥t❡ ❛❧ r✐❧❡✈❛t♦r❡✳

❙✐ ✐♥❝♦♥tr❛♥♦ ❛♥❝❤❡ ✐ t❡r♠✐♥✐ Solarimetro ❡Attinometro✿ ✐❧ ♣r✐♠♦ ♣✉ò ❡ss❡r❡ ❣❡♥❡r❛❧♠❡♥t❡

✐♥t❡r♣r❡t❛t♦ ❝♦♠❡ ❡q✉✐✈❛❧❡♥t❡ ❛❧ Piranometro✱ ♠❡♥tr❡ ✐❧ s❡❝♦♥❞♦ s✐ r✐❢❡r✐s❝❡ ❞✐ s♦❧✐t♦ ❛❧

Pireliometro✳

◗✉❡st✐ str✉♠❡♥t✐ ❝♦♥✈❡rt♦♥♦ ❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ✐♥ ✉♥✬❛❧tr❛ ❢♦r♠❛ ❞✐ ❡♥❡r❣✐❛ ❡ ❢♦r♥✐s❝♦♥♦

❧❛ ♠✐s✉r❛ ❞❡❧ ✢✉ss♦ ❞✐ ❡♥❡r❣✐❛ ♣r♦❞♦tt♦ ❞❛❧❧❛ r❛❞✐❛③✐♦♥❡✳ ❊s✐st♦♥♦ ❞✐✈❡rs❡ r❛ss❡❣♥❡ ❞❡❣❧✐

str✉♠❡♥t✐ ♣❡r ❧❛ ♠✐s✉r❛ ❞✐ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡✿ ❛❞ ❡s❡♠♣✐♦ ▼♦r✐❦♦❢❡r ✭✶✾✺✽✮✱ ❉r✉♠♠♦♥❞

✭✶✾✻✹✮ ❡ ❨❡❧❧♦t ✭✶✾✻✼✮✳

■ ♣✐r❛♥♦♠❡tr✐ ♣✐ù ✉s❛t✐ ♦❣❣✐ s♦♥♦ ❜❛s❛t✐ s✉❧❧❛ ♠✐s✉r❛ ❞❡❧❧❛ ❞✐✛❡r❡♥③❛ ❞✐ t❡♠♣❡r❛t✉r❛ ❞✐

❞✉❡ s✉♣❡r✜❝✐✱ ✉♥❛ ♥❡r❛ ✭❝❤❡ ❛ss♦r❜❡ ❧❛ ♠❛❣❣✐♦r ♣❛rt❡ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡✮ ❡ ✉♥❛ ❜✐❛♥❝❛

✭❝❤❡ r✐✢❡tt❡ ❧❛ ♠❛❣❣✐♦r ♣❛rt❡ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡✮❀ ❧❛ ❞✐✛❡r❡♥③❛ ❞✐ t❡♠♣❡r❛t✉r❛ ✈✐❡♥❡

r✐❧❡✈❛t❛ ♠❡❞✐❛♥t❡ t❡r♠♦❝♦♣♣✐❡✳ ❖♣♣♦rt✉♥❛♠❡♥t❡ ♣r♦t❡tt❡ ❞❛❧ ✈❡♥t♦ ❡ ❝♦♠♣❡♥s❛t❡ ❝♦♥tr♦

✈❛r✐❛③✐♦♥✐ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ❛♠❜✐❡♥t❡✱ ❧❡ t❡r♠♦❝♦♣♣✐❡ ❢♦r♥✐s❝♦♥♦ ❞✐r❡tt❛♠❡♥t❡ ✉♥ s❡❣♥❛❧❡

❡❧❡ttr✐❝♦ ❞❡❧❧✬♦r❞✐♥❡ ❞❡✐ ♠✐❧❧✐✈♦❧t ❝❤❡ ♣✉ò ❡ss❡r❡ ❢❛❝✐❧♠❡♥t❡ r✐❧❡✈❛t♦✱ r❡❣✐str❛t♦ ❡ ✐♥t❡r❣r❛t♦

♥❡❧ t❡♠♣♦✳

■ ♣✐r❛♥♦♠❡tr✐ ❝♦♠✉♥❡♠❡♥t❡ ✉s❛t✐ ♥❡❣❧✐ ❙t❛t✐ ❯♥✐t✐ s♦♥♦ ❣❧✐Eppley ❡ ✐ Spectrolab Instruments✱

✐♥ ❊✉r♦♣❛ ✐ Moll − Gorczynski✱ ✐♥ ❘✉ss✐❛ ✐ Y anishevskiy ❡❞ ✐♥ ❆✉str❛❧✐❛ ✐ Thickett −

Norris ✭Groiss✮✳ ■❧ piranometro Eppley 180◦ ❡r❛ ❧♦ str✉♠❡♥t♦ ♣✐ù ✉s❛t♦ ♣r❡ss♦ ❧❡ st❛③✐♦♥✐

❞✐ r✐❧❡✈❛♠❡♥t♦ ♠❡t❡r❡♦❧♦❣✐❝♦✳ ❊ss♦ ✉s❛✈❛ ✉♥ r✐✈❡❧❛t♦r❡ ❛ ❞✉❡ ❛♥❡❧❧✐ ❝♦♥❝❡♥tr✐❝✐ ❞✐ ❛r❣❡♥t♦

❞✐ s♣❡ss♦r❡ ❞✐ 0.25 mm✱ ♦♣♣♦rt✉♥❛♠❡♥t❡ r✐✈❡st✐t✐ ❞✐ ❜✐❛♥❝♦ ❡ ♥❡r♦✳ ▲✬❛♥❡❧❧♦ ❡st❡r♥♦ ❡r❛

r✐❝♦♣❡rt♦ ❝♦♥ ♦ss✐❞♦ ❞✐ ♠❛❣♥❡s✐♦ ❝❤❡ r✐✢❡tt❡ ❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡✱ ♠❡♥tr❡ ❧✬❛♥❡❧❧♦ ✐♥t❡r♥♦

❝♦♥ ♥❡r♦ ❞✐ Parson ❝❤❡ ❛ss♦r❜❡ ❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡✳ ▲❛ ❞✐✛❡r❡♥③❛ ❞✐ t❡♠♣❡r❛t✉r❛ tr❛

q✉❡st✐ ❞✉❡ ❛♥❡❧❧✐ ❡r❛ r✐❧❡✈❛t❛ ❝♦♥ t❡r♠♦♣✐❧❡ ❡ r❛♣♣r❡s❡♥t❛✈❛ ❧❛ ♠✐s✉r❛ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ s♦✲

❧❛r❡ ❛ss♦r❜✐t❛✳ ▲❛ s✐♠♠❡tr✐❛ ❝✐r❝♦❧❛r❡ ♠✐♥✐♠✐③③❛✈❛ ❣❧✐ ❡✛❡tt✐ ❞❡❧❧✬❛♥❣♦❧♦ ❞✐ ❛③✐♠✉t❤ s✉❧❧❛

r✐s♣♦st❛ ❞❡❧❧♦ str✉♠❡♥t♦✳ ■❧ r✐❧❡✈❛t♦r❡ ❡r❛ ♣♦st♦ ✐♥ ✉♥ ❜✉❧❜♦ ❞✐ ✈❡tr♦ q✉❛s✐ s❢❡r✐❝♦✱ ❝♦♥ ✉♥❛

✺✽

tr❛s♠✐ss✐♦♥❡ ♠❛❣❣✐♦r❡ ❞✐ 0.90 ♣❡r ❛❧❧❛ ♠❛❣❣✐♦r ♣❛rt❡ ❞❡❧❧♦ s♣❡ttr♦ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡✳

▲❛ r✐s♣♦st❛ ❞✐ q✉❡st♦ ♠♦❞❡❧❧♦ Eppley ❡r❛ ❞✐♣❡♥❞❡♥t❡ ❞❛❧❧❛ t❡♠♣❡r❛t✉r❛ ❛♠❜✐❡♥t❡✱ ❝♦♥

✉♥❛ s❡♥s✐❜✐❧✐tà ❞❡❝r❡s❝❡♥t❡ ❞❛ 0.05 ✪ ❛ 0.15% ♣❡r ◦C ✭Coulson 1975✮✳ ❙✐ è ♣r♦❝❡❞✉t♦ ❛❞

❛❣❣✐✉♥❣❡r❡ ✉♥❛ ❝♦♠♣❡♥s❛③✐♦♥❡ ❞✐ t❡♠♣❡r❛t✉r❛ ❛❧ ❝✐r❝✉✐t♦ ❡st❡r♥♦ ❡❞ ❡❧✐♠✐♥❛r❡ q✉❡st♦ ❡r✲

r♦r❡✳ ■❧ ♣✐r❛♥♦♠❡tr♦ Eppley 180◦ ♥♦♥ è ♣✐ù ✐♥ ♣r♦❞✉③✐♦♥❡ ❡❞ è st❛t♦ s♦st✐t✉✐t♦ ❞❛❧ ♠♦❞❡❧❧♦

Black and White✳

■❧ ♣✐r❛♥♦♠❡tr♦ Eppley Black and White ✭❋✐❣✉r❛ ✸✳✶✶ ✮ ✉t✐❧✐③③❛ t❡r♠♦♣✐❧❡ ❝♦♥ ❣✐✉♥③✐♦♥✐

❢r❡❞❞❡ ❡ ❝❛❧❞❡ r✐❝♦♣❡rt❡ ❝♦♥ ♥❡r♦ ❞✐ Parson ❡ s♦❧❢❛t♦ ❞✐ ❜❛r✐♦ ❡❞ ❤❛♥♥♦ ✉♥❛ ♠✐❣❧✐♦r❡ r✐s♣♦st❛

❛♥❣♦❧❛r❡✳ Pr❡s❡♥t❛ ✉♥❛ ❝♦♣❡rt✉r❛ ✐♥ ✈❡tr♦ ❡❞ è ✐♥ ❣r❛❞♦ ❞✐ ♠❛♥t❡♥❡r❡ ✉♥❛ ♣r❡❝✐s✐♦♥❡ ❞✐

±1.5% ♣❡r ✉♥ r❛♥❣❡ ❞✐ t❡♠♣❡r❛t✉r❛ ❝♦♠♣r❡s♦ tr❛ −20 ❡ +40◦C✳

❋✐❣✉r❛ ✸✳✶✶✿ P✐r❛♥♦♠❡tr♦ Eppley Black and White

❯♥ ❛❧tr♦ ♠♦❞❡❧❧♦ ❞✐ ♣✐r❛♥♦♠❡tr♦ ✐♥ ♣r♦❞✉③✐♦♥❡ è ❧✬Eppley Precision Spectral (PSP )

✭❋✐❣✉r❛ ✸✳✶✷ ✮ ❝❤❡ ✉t✐❧✐③③❛ ✉♥❛ t❡r♠♦♣✐❧❛ ❝♦♠❡ r✐❧❡✈❛t♦r❡✱ ❞✉❡ ❝♦♣❡rt✉r❡ ❝♦♥❝❡♥tr✐❝❤❡ ❡♠✐✲

s❢❡r✐❝❤❡ ❡❞ è ✐♥ ❣r❛❞♦ ❞✐ ♠❛♥t❡♥❡r❡ ✉♥❛ ♣r❡❝✐s✐♦♥❡ ❞✐ ±0.5% ♣❡r ✉♥ r❛♥❣❡ ❞✐ t❡♠♣❡r❛t✉r❛

❝♦♠♣r❡s♦ tr❛ −20 ❡ +40➦❈✳

■❧ s♦❧❛r✐♠❡tr♦ Moll−Gorczynski è ✉♥ ♣✐r❛♥♦♠❡tr♦ ❜❛s❛t♦ s✉ t❡r♠♦❝♦♣♣✐❡ ❛✈❡♥t✐ ❧❛ ❣✐✉♥✲

③✐♦♥❡ ❝❛❧❞❛ ❡s♣♦st❛ ❛❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ❡ ❧❛ ❣✐✉♥③✐♦♥❡ ❢r❡❞❞❛ s❝❤❡r♠❛t❛ ❛❧❧❛ r❛❞✐❛③✐♦♥❡✳

❯♥ ❛❧tr♦ t✐♣♦ ❞✐ ♣✐r❛♥♦♠❡tr♦✱ ✐❧ Robitsch✱ è ❜❛s❛t♦ s✉❧❧❛ ❞✐❧❛t❛③✐♦♥❡ ❞✐✛❡r❡♥③✐❛❧❡ ❞✐ ❧❛♠✐♥❡

❜✐♠❡t❛❧❧✐❝❤❡ ❡s♣♦st❡ ❛❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡❀ q✉❡st♦ ♠❡t♦❞♦ ♦✛r❡ ✐❧ ✈❛♥t❛❣❣✐♦ ❞✐ ❝♦♥s❡♥t✐r❡✱

✐♥ ③♦♥❡ ♥♦♥ s❡r✈✐t❡ ❞❛ ✉♥❛ r❡t❡ ❡❧❡ttr✐❝❛✱ ❧✬♦♣❡r❛③✐♦♥❡ ❞✐r❡tt❛ ❞✐ r❡❣✐str❛t♦r✐ ♠❡❝❝❛♥✐❝✐

✺✾

❋✐❣✉r❛ ✸✳✶✷✿ P✐r❛♥♦♠❡tr♦ Eppley Precision Spectral (PSP )

❛ ♠♦❧❧❛✳ ❘❛❞✐♦♠❡tr✐ ❛ ❞✐❧❛t❛③✐♦♥❡ t❡r♠✐❝❛ s♦♥♦ ❝♦♠✉♥❡♠❡♥t❡ ✉s❛t✐ ✐♥ st❛③✐♦♥✐ ✐s♦❧❛t❡ ❡

s❡❜❜❡♥❡ ♥♦♥ s✐❛♥♦ ♠♦❧t♦ ♣r❡❝✐s✐✱ s♦♥♦ ❧❛ ♣r✐♥❝✐♣❛❧❡ ❢♦♥t❡ ❞❡✐ ❞❛t✐ s✉❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡

♣❡r ✐ ♣❛❡s✐ ❛❧ ❞✐ ❢✉♦r✐ ❞❡❧❧✬❊✉r♦♣❛✱ ❞❡❧❧✬❆✉str❛❧✐❛✱ ❞❡❧ ●✐❛♣♣♦♥❡ ❡ ❞❡❧❧✬❆♠❡r✐❝❛ ❞❡❧ ◆♦r❞✳

❱✐ s♦♥♦ ❛♥❝❤❡ ♣✐r❛♥♦♠❡tr✐ ❜❛s❛t✐ s✉ r✐✈❡❧❛t♦r✐ ❛❞ ❡✛❡tt♦ ❢♦t♦✈♦❧t❛✐❝♦ ✭❝❡❧❧❡ s♦❧❛r✐ ❛❧ s✐❧✐❝✐♦✮✿

❛❞ ❡s❡♠♣✐♦ ✐❧ s♦❧❛r✐♠❡tr♦ ❞✐ Y ellot✳

◆❡❧❧❛ ❝❛♠♣❛❣♥❛ ❞✐ ♠✐s✉r❡ s♣❡r✐♠❡♥t❛❧✐ s✐ s♦♥♦ ✐♠♣✐❡❣❛t✐ ❞✉❡ ♣✐r❛♥♦♠❡tr✐ Eppley Black

and White 8 − 48 ❝♦❧❧❡❣❛t✐ ❛❞ ✉♥ ♠✉❧t✐♠❡tr♦ ❞✐❣✐t❛❧❡ ♣❡r ❧✬❛❝q✉✐s✐③✐♦♥❡ ❡ ❧✬❡❧❛❜♦r❛③✐♦♥❡

❞❡✐ ❞❛t✐✳ ❈♦♠❡ ♠♦str❛t♦ ✐♥ ❋✐❣✉r❛ ✷✳✶✵ s✐ è ♣♦st♦ ✉♥ ♣✐r❛♥♦♠❡tr♦✱ s1✱ ♥❡❧❧✬❛♠❜✐❡♥t❡

s❡♠✐❝♦♥✜♥❛t♦ ❛❧ ❞✐ s♦tt♦ ❧❛ ❝♦♣❡rt✉r❛ ✐♥ ✈❡tr♦✱ ❧✬❛❧tr♦✱ s2✱ ♥❡❧❧♦ s♣❛③✐♦ ❛♣❡rt♦ ❝r❡❛t♦ ❞❛❧✲

❧✬✐♥t❡rr✉③✐♦♥❡ ❞❡❧❧❛ str✉tt✉r❛✳ ▲❡ s♣❡❝✐✜❝❤❡ t❡❝♥✐❝❤❡ ❞❡❧ ♠♦❞❡❧❧♦ ✽ ✲ ✹✽ s♦♥♦ r✐❛ss✉♥t❡ ✐♥

❚❛❜❡❧❧❛ ✸✳✼✳

❙❡♥s✐❜✐❧✐tà 11µV/Wm−2

■♠♣❡❞❡♥③❛ 350ohm

❉✐♣❡♥❞❡♥③❛ ❞❛❧❧❛ t❡♠♣❡rt✉r❛ ±1.5% ❞❛ −20 ❛ +40◦C

▲✐♥❡❛r✐tà ±1% ❞❛ ✵ ❛ ✶✹✵✵ W/m2

❚❡♠♣♦ ❞✐ r✐s♣♦st❛ ✸ ♦ ✹ s❡❝♦♥❞✐

❘✐s♣♦st❛ ❞✐r❡③✐♦♥❛❧❡±2% 0÷ 70◦C r✐s♣❡tt♦ ❛❧❧♦ ③❡♥✐t❤✱±5% 70÷ 80◦C r✐s♣❡tt♦ ❛❧❧♦ ③❡♥✐t❤

❚❛❜❡❧❧❛ ✸✳✼✿ ❙♣❡❝✐✜❝❤❡ t❡❝♥✐❝❤❡ ♣✐r❛♥♦♠❡tr♦ Eppley Black and White 8− 48

✻✵

✹ ❈♦♥❢r♦♥t♦ tr❛ r✐s✉❧t❛t✐ s♣❡r✐♠❡♥t❛❧✐ ❡ s✐♠✉❧❛t✐

▲❡ ♠✐s✉r❛③✐♦♥✐ s♦♥♦ st❛t❡ ❡✛❡tt✉❛t❡ ❛✈✈❛❧❡♥❞♦s✐ ❞❡❧❧❛ ❝❡♥tr❛❧✐♥❛ ♣❡r r✐❧❡✈❛③✐♦♥✐ ♠✐❝r♦✲

❝❧✐♠❛t✐❝❤❡ ❉❡❧t❛❖❍▼ ❍❉✸✷✳✶ ❡q✉✐♣❛❣❣✐❛t❛ ❝♦♥ s❡♥s♦r❡ ❞✐ t❡♠♣❡r❛t✉r❛ ❞❡❧❧✬❛r✐❛✱ ❛♥❡♠♦✲

♠❡tr♦ ♣❡r ❧❛ ♠✐s✉r❛ ❞❡❧❧❛ ✈❡❧♦❝✐tà ❞❡❧ ✈❡♥t♦✱ s❡♥s♦r❡ ❝❛♣❛❝✐t✐✈♦ ♣❡r ❧❛ ♠✐s✉r❛ ❞❡❧❧✬✉♠✐❞✐tà

r❡❧❛t✐✈❛ ❡ ❣❧♦❜♦t❡r♠♦♠❡tr♦✱ ♣♦s✐③✐♦♥❛t❛ ❛❧ ❞✐ s♦tt♦ ❞❡❧❧❛ ❝♦♣❡rt✉r❛ ❡q✉✐❞✐st❛♥t❡ ❞❛❧❧❡ ❞✉❡

❛♣❡rt✉r❡ ❧❛t❡r❛❧✐ ❡ ❝♦♥ ❧❡ s♦♥❞❡ ♣♦st❡ ❛❞ ✉♥✬❛❧t❡③③❛ ❞✐ 1.1 m ❝✐r❝❛ ❞❛ t❡rr❛✳ P❡r r✐❧❡✈❛r❡

❧✬❛♥❞❛♠❡♥t♦ ❞❡❧❧❛ t❡r♠♣❡r❛t✉r❛ ❞❡❧❧❡ s✉♣❡r✜❝✐❡ ✐♥t❡r♥❛ ❞❡❧❧❛ ❝♦♣❡rt✉r❛ ❡ ❞❡❧ ❜❛s❛♠❡♥t♦

s♦♥♦ st❛t❡ ✐♥st❛❧❧❛t❡ ❞✉❡ t❡r♠♦❝♦♣♣✐❡ t✐♣♦ ❏ ❝♦❧❧❡❣❛t❡ ❛❞ ✉♥ ♠✉❧t✐♠❡tr♦ ❞✐❣✐t❛❧❡✳ P❡r ❧❛

♠✐s✉r❛ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ t♦t❛❧❡ ✭❞✐r❡tt❛ ❡ ❞✐✛✉s❛✮ ♥❡❧❧♦ s♣❛③✐♦ s❡♠✐❝♦♥✜♥❛t♦ ❛❧ ❞✐

s♦tt♦ ❞❡❧❧❛ ❝♦♣❡rt✉r❛ ❡ ♥❡❧❧♦ s♣❛③✐♦ ❛♣❡rt♦ ❛❧❧✬❡st❡r♥♦✱ s✐ s♦♥♦ ✐♠♣✐❡❣❛t✐ ❞✉❡ s♦❧❛r✐♠❡tr✐

❊♣♣❧❡② ❇❧❛❝❦ ❛♥❞ ❲❤✐t❡ ✽✲✹✽ ✐♥t❡r❢❛❝❝✐❛t✐ ❛♥❝❤✬❡ss✐ ❝♦♥ ✐❧ ♠✉❧t✐♠❡tr♦ ❞✐❣✐t❛❧❡✳ ▲❛ ❝❡♥tr❛❧✐✲

♥❛ ♠✐❝r♦❝❧✐♠❛t✐❝❛ ❛❝q✉✐s✐✈❛ ✐❧ ❞❛t♦ ❞❛❧❧❡ s♦♥❞❡ ♦❣♥✐ 15 s✱ ♠❡♥tr❡ t❡r♠♦❝♦♣♣✐❡ ❡ s♦❧❛r✐♠❡tr✐

❛✈❡✈❛♥♦ ✉♥❛ ❢r❡q✉❡♥③❛ ❞✐ ❝❛♠♣✐♦♥❛♠❡♥t♦ ❞✐ 1 Hz✳ ■♥ ❋✐❣✉r❛ ✹✳✶ s✐ r✐♣♦rt❛ ❧♦ s❝❤❡♠❛ ❞✐

♣♦s✐③✐♦♥❛♠❡♥t♦ ❞❡❧❧❡ s♦♥❞❡✳

❋✐❣✉r❛ ✹✳✶✿ ❙❝❤❡♠❛ ❞✐ ♣♦s✐③✐♦♥❛♠❡♥t♦ ❞❡❧❧❡ s♦♥❞❡✿ ✐♥ r♦ss♦ ❧❛ ❝❡♥tr❛❧✐♥❛ ♠✐❝r♦❝❧✐♠❛♥t✐❝❛✱✐♥ ❛③③✉rr♦ ❧❛ t❡r♠♦❝♦♣♣✐❛ ❞❡❧❧❛ ❝♦♣❡rt✉r❛✱ ✐♥ ✈✐♦❧❛ ❧❛ t❡r♠♦❝♦♣♣✐❛ ❞❡❧ ♣❛✈✐♠❡♥t♦ ❡❞ ✐♥❣✐❛❧❧♦ ❡❞ ✐♥ ❛r❛♥❝✐♦♥❡ ✐ ❞✉❡ s♦❧❛r✐♠❡tr✐ s♦tt♦ ❡❞ ❛❧❧✬❡st❡r♥♦ ❞❡❧❧❛ ❝♦♣❡rt✉r❛✱ r✐s♣❡tt✐✈❛♠❡♥t❡✭●♦♦❣❧❡ ❊❛rt❤ ✻✳✶✱ ✾✲✶✶✲✷✵✶✷✮

✻✶

■♥♦❧tr❡ ♣❡r ❧❛ ❞❡✜♥✐③✐♦♥❡ ❞❡❧❧❡ ❝♦♥❞✐③✐♦♥✐ ❛❧ ❝♦♥t♦r♥♦ ❞❡❧ ♠♦❞❡❧❧♦ s♦♥♦ st❛t✐ ✉t✐❧✐③③❛t✐ ❛♥❝❤❡

✐ ❞❛t✐ ❝❧✐♠❛t✐❝✐ ♠❡❞✐ ♦r❛r✐ r✐❧❡✈❛t✐ ❞❛ ❆❘P❆ ✭❆❣❡♥③✐❛ ❘❡❣✐♦♥❛❧❡ Pr❡✈❡♥③✐♦♥❡ ❡ ❆♠❜✐❡♥t❡

❞❡❧❧✬❊♠✐❧✐❛ ❘♦♠❛❣♥❛✮ ♣r❡ss♦ ❧❛ st❛③✐♦♥❡ ♠❡t❡r❡♦❧♦❣✐❝❛ ✉r❜❛♥❛✳

❙✐ r✐♣♦rt❛♥♦ ❧❛ ❝❛r❛tt❡r✐③③❛③✐♦♥❡ ❞❡❧❧✬❛♠❜✐❡♥t❡ t❡r♠✐❝♦ ❛❧ ❞✐ s♦tt♦ ❞❡❧❧❛ ❝♦♣❡rt✉r❛✱ ✐ r✐s✉❧✲

t❛t✐ ❞❡❧❧❡ s✐♠✉❧❛③✐♦♥✐ ❝♦♥t❡st✉❛❧✐③③❛t❡ ♥❡✐ ❣✐♦r♥✐ ❡❞ ♥❡❣❧✐ ✐♥t❡r✈❛❧❧✐ ♦r❛r✐ ❞❡❧❧❡ r✐❧❡✈❛③✐♦♥✐✱

❧✬❛♥❞❛♠❡♥t♦ ❞❡✐ ♣❛r❛♠❡tr✐ ♦❣❣❡tt♦ ❞✐ ♠✐s✉r❛③✐♦♥✐ ❡❞ ✐❧ ❝♦♥❢r♦♥t♦ ❝r✐t✐❝♦ ❝♦♥ ✐ r✐s✉❧t❛t✐ ❞❡❧

♠♦❞❡❧❧♦ ❞✐ ❝❛❧❝♦❧♦ ♣❡r ✉♥ ❣✐♦r♥♦ s♦❧❡❣❣✐❛t♦ t✐♣✐❝❛♠❡♥t❡ ❡st✐✈♦ ✭✸✵ ▲✉❣❧✐♦ ✷✵✶✷✮ ❡ ♣❡r ✉♥❛

❣✐♦r♥❛t❛ ❧✐♠♣✐❞❛ ♣r✐♠❛✈❡r✐❧❡ ✭✷✻ ▼❛r③♦ ✷✵✶✷✮✳

✻✷

✹✳✶ ●✐♦r♥♦ ✸✵ ▲✉❣❧✐♦ ✷✵✶✷

▲❡ r✐❧❡✈❛③✐♦♥✐ s♣❡r✐♠❡♥t❛❧✐ ❞❡✐ ❞❛t✐ ♠✐❝r♦❝❧✐♠❛t✐❝✐ r✐❣✉❛r❞❛♥♦ ✐❧ ❣✐♦r♥♦ 30 Luglio 2012

tr❛ ❧❡ ♦r❡ 11 : 00 ❡ ❧❡ ♦r❡ 14 : 00 ✭♦r❛ s♦❧❛r❡✮✳ ■♥ ❋✐❣✉r❛ ✹✳✷ s✐ r✐♣♦rt❛ ❧✬❛♥❞❛♠❡♥t♦✱

✐♥ ❢✉♥③✐♦♥❡ ❞❡❧ t❡♠♣♦✱ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ❡st❡r♥❛ ♠✐s✉r❛t❛✱ ❡❧❛❜♦r❛t❛ ❡ s❝♦♠♣♦st❛✱

❛♣♣❧✐❝❛♥❞♦ ❧❡ ❡q✉❛③✐♦♥✐ ♠♦str❛t❡ ♥❡❧ ♣❛r❛❣r❛❢♦ ✷✳✹✳✸ ❈❛❧❝♦❧✐ s✉❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡✱ ♥❡❧❧❡

❝♦♠♣♦♥❡♥t✐ ❞✐r❡tt❛ ❡ ❞✐✛✉s❛✱ ♥❡❧❧♦ s♣❛③✐♦ ❛♣❡rt♦ ♦✛❡rt♦ ❞❛❧❧✬✐♥t❡rr✉③✐♦♥❡ ❞❡❧❧❛ str✉tt✉r❛❀

✐♥♦❧tr❡ ✐♥ ❋✐❣✉r❛ ✹✳✷ s✐ r✐♣♦rt❛ ❧✬❛♥❞❛♠❡♥t♦✱ ✐♥ ❢✉♥③✐♦♥❡ ❞❡❧ t❡♠♣♦✱ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡

t♦t❛❧❡ ❛❧ ❞✐ s♦tt♦ ❞❡❧❧❛ ❝♦♣❡rt✉r❛✳ ■ ❞❛t✐ r❡❧❛t✐✈✐ ❛❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ❡st❡r♥❛✱ ❡❧❛❜♦r❛t✐

♣❡r t❡♥❡r ❝♦♥t♦ ❞❡❧❧✬✐♥❝❧✐♥❛③✐♦♥❡ β ❞❡❧❧❛ s✉♣❡r✜❝✐❡ ❞❡❧❧❛ ❝♦♣❡rt✉r❛✱ ✉♥✐t❛♠❡♥t❡ ❛✐ ✈❛❧♦r✐

❝❛❧❝♦❧❛t✐ ❞❡❧❧✬❛♥❣♦❧♦ ❞✐ ✐♥❝✐❞❡♥③❛ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡✱ ❝♦♥❝♦rr♦♥♦ ❛❧❧❛ ❞❡✜♥✐③✐♦♥❡ ❞❡❧❧❡

❝♦♥❞✐③✐♦♥✐ ❛❧ ❝♦♥t♦r♥♦ ❞❡❧ ♠♦❞❡❧❧♦ ❞✐ ❝❛❧❝♦❧♦✳ ■ ✈❛❧♦r✐ ❞✐ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ❡st❡r♥❛ ❡ ❞✐

r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ s♦tt♦ ❧❛ ❝♦♣❡rt✉r❛ s♦♥♦ st❛t✐ ✐♠♣✐❡❣❛t✐ ♣❡r ❧❛ ❝❛r❛tt❡r✐③③❛③✐♦♥❡ ❞❡❧❧❛

❝♦♣❡rt✉r❛ st❡ss❛ s❡❝♦♥❞♦ q✉❛♥t♦ r✐♣♦rt❛t♦ ♥❡❧ ♣❛r❛❣r❛❢♦ ✷✳✺ Pr♦♣r✐❡tà ❞❡❧❧❛ ❝♦♣❡rt✉r❛ ✐♥

✈❡tr♦✳

❋✐❣✉r❛ ✹✳✷✿ ❘❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ❡st❡r♥❛ ❞✐r❡tt❛ ❡ ❞✐✛✉s❛ ❡ r❛❞✐❛③✐♦♥❡ t♦t❛❧❡ s♦tt♦ ❧❛ ❝♦♣❡rt✉r❛✱✸✵ ▲✉❣❧✐♦ ✷✵✶✷

■♥ ❋✐❣✉r❛ ✹✳✷ s✐ ♦ss❡r✈❛ ✉♥ ❛♥❞❛♠❡♥t♦ ♦s❝✐❧❧❛t♦r✐♦ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ t♦t❛❧❡ s♦tt♦ ❧❛ ❝♦♣❡rt✉r❛

❞♦✈✉t❛ ❛❧❧❛ ♣❡r✐♦❞✐❝❛ ✐♥t❡r❝❡tt❛③✐♦♥❡ ❞❛ ♣❛rt❡ ❞❡❧ s♦❧❛r✐♠❡♥tr♦ ❞❡❧❧✬♦♠❜r❡❣❣✐❛t✉r❛ ❞♦✈✉t❛

✻✸

❛❣❧✐ ❡❧❡♠❡♥t✐ ❞❡❧❧❛ str✉tt✉r❛ ♣♦rt❛♥t❡ ❡❞ ❛❧❧❡ s❡r✐❣r❛✜❡ s♦✈r❛♣♣♦st❡ ❛✐ ♣❛♥♥❡❧❧✐ ✐♥ ✈❡tr♦✳

■♥ ❋✐❣✉r❛ ✹✳✸ s✐ r✐♣♦rt❛ ❧✬❛♥❞❛♠❡♥t♦✱ ✐♥ ❢✉♥③✐♦♥❡ ❞❡❧ t❡♠♣♦✱ ❞❡❧❧❛ ✈❡❧♦❝✐tà ❞❡❧❧✬❛r✐❛ ♠✐s✉r❛✲

t❛ s♦tt♦ ❧❛ ❝♦♣❡rt✉r❛✱ ♥❡❝❡ss❛r✐❛ ♣❡r ✐❧ ❝❛❧❝♦❧♦ ❞❡✐ ❝♦❡✣❝✐❡♥t✐ ❞✐ s❝❛♠❜✐♦ t❡r♠✐❝♦ ❝♦♥✈❡tt✐✈♦

❡ ♣❡r ❧✬❛♥❛❧✐s✐ ❞❡❧❧❡ ❝♦♥❞✐③✐♦♥✐ ❞✐ ❝♦♠❢♦rt t❡r♠✐❝♦ ♥❡❧❧✬❛♠❜✐❡♥t❡ s❡♠✐❝♦♥✜♥❛t♦✳

❋✐❣✉r❛ ✹✳✸✿ ❱❡❧♦❝✐tà ❞❡❧❧✬❛r✐❛ ♠✐s✉r❛t❛ s♦tt♦ ❧❛ ❝♦♣❡rt✉r❛✱ ✸✵ ▲✉❣❧✐♦ ✷✵✶✷

■♥ ❚❛❜❡❧❧❛ ✹✳✶ s✐ r✐♣♦rt❛♥♦ ✐ ❞❛t✐ ❝❧✐♠❛t✐❝✐ ♠❡❞✐ ♦r❛r✐ r✐❧❡✈❛t✐ ❞❛ ❆❘P❆ ♣r❡ss♦ ❧❛

st❛③✐♦♥❡ ♠❡t❡r❡♦❧♦❣✐❝❛ ✉r❜❛♥❛ ❝❤❡ ❝♦♠♣❧❡t❛♥♦ ❧❡ ❝♦♥❞✐③✐♦♥✐ ❛❧ ❝♦♥t♦r♥♦ ❞❡❧ ♠♦❞❡❧❧♦ ❞✐

❝❛❧❝♦❧♦✿ t❡♠♣❡r❛t✉r❛ ❞❡❧❧✬❛r✐❛ ❡st❡r♥❛ Te✱ ✉♠✐❞✐tà r❡❧❛t✐✈❛ ❡st❡r♥❛ UR✱ ✈❡❧♦❝✐tà ❞❡❧ ✈❡♥t♦

❡st❡r♥♦ Va✳ ■♥♦❧tr❡ s❡♠♣r❡ ✐♥ ❚❛❜❡❧❧❛ ✹✳✶ s✐ r✐♣♦rt❛ ❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧❧❛ ✈♦❧t❡ ❝❡❧❡st❡

❛❧❧✬✐♥✜♥✐t♦ Tsky ♦tt❡♥✉t❛ ❞❛❧❧❛ r❛❝❝♦❧t❛ ❞✐ ❞❛t✐ ❝❧✐♠❛t✐❝✐ ▼❡t❡♦♥♦r♠ ❬✶✸❪✳

Ora Te (◦C) UR (%) Va (m/s) Tsky (◦C)

✶✶ 29.8 44 2 14.55

✶✷ 31 39 2.2 16.93

✶✸ 31.6 36 1.8 14.85

✶✹ 32.2 31 2 15.67

✶✺ 32.8 31 2.4 16.54

❚❛❜❡❧❧❛ ✹✳✶✿ ❉❛t✐ ❝❧✐♠❛t✐❝✐ ♠❡❞✐ ♦r❛r✐ r✐❧❡✈❛t✐ ❞❛ ❆❘P❆ ❡ t❡♠♣❡r❛t✉r❛ ❞❡❧❧❛ ✈♦❧t❛ ❝❡❧❡st❡❛❧❧✬✐♥✜♥✐t♦ ❞❛ ▼❡t❡♦♥♦r♠✱ ✸✵ ▲✉❣❧✐♦ ✷✵✶✷

✻✹

▲❛ s♦❧✉③✐♦♥❡ ♥✉♠❡r✐❝❛ ❞❡❧ ♠♦❞❡❧❧♦✱ ✐♥ ♣❛rt✐❝♦❧❛r❡ ❧✬✐♥t❡❣r❛③✐♦♥❡ ❞❡❧❧❡ ❡q✉❛③✐♦♥✐ ✭✷✳✶ ✮✱

✭✷✳✼ ✮ ❡ ✭✷✳✽ ✮ ❝♦♥ ❧❡ r❡❧❛t✐✈❡ ❝♦♥❞✐③✐♦♥✐ ❛❧ ❝♦♥t♦r♥♦✱ ❡❞ ✐❧ ❝❛❧❝♦❧♦✱ ✐♥ ❢✉♥③✐♦♥❡ ❞❡❧ t❡♠♣♦✱ ❞❡✐

♣❛r❛♠❡tr✐ ♠✐❝r♦❝❧✐♠❛t✐❝✐ ❞✐ ✐♥t❡r❡ss❡ ♣❡r ❧❛ ❝❛r❛tt❡r✐③③❛③✐♦♥❡ ❞❡❧❧✬❛♠❜✐❡♥t❡ t❡r♠✐❝♦ s❡♠✐✲

❝♦♥✜♥❛t♦✱ s♦♥♦ ❛✣❞❛t✐ ❛❞ ✉♥ ❝♦❞✐❝❡ ❞✐ ❝❛❧❝♦❧♦ s✈✐❧✉♣♣❛t♦ ✐♥ ❛♠❜✐❡♥t❡ ▼❛t❧❛❜ ✭❆♣♣❡♥❞✐❝❡

❆✮✳ ▲❡ ❝♦♥❞✐③✐♦♥✐ ✐♥✐③✐❛❧✐ ❛ss✉♥t❡✱ r✐♣♦rt❛t❡ ✐♥ ❚❛❜❡❧❧❛ ✹✳✷✱ s♦♥♦ ❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧❧✬❛r✐❛

Ti ♥❡❧❧♦ s♣❛③✐♦ s❡♠✐❝♦♥✜♥❛t♦✱ ❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧❧❛ s✉♣❡r✜❝✐❡ ✐♥t❡r♥❛ ❞❡❧❧❛ ❝♦♣❡rt✉r❛ Tr,i

❡ ❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧❧❛ s✉♣❡r✜❝✐❡ ❞❡❧ ♣❛✈✐♠❡♥t♦ Tm ♦tt❡♥✉t❡ ❞❛❧❧❡ r✐❧❡✈❛③✐♦♥✐ str✉♠❡♥t❛❧✐

❛❧❧❡ ♦r❡ ✶✶✿✵✵✳

Ti (◦C) Tr,i (

◦C) Tm (◦C)

29.50 45.56 37.29

❚❛❜❡❧❧❛ ✹✳✷✿ ❈♦♥❞✐③✐♦♥✐ ✐♥✐③✐❛❧✐ ❞❡❧ ♠♦❞❡❧❧♦✱ ✸✵ ▲✉❣❧✐♦ ✷✵✶✷

■♥ ❋✐❣✉r❛ ✹✳✹ s✐ r✐♣♦rt❛♥♦ ❣❧✐ ❛♥❞❛♠❡♥t✐✱ ✐♥ ❢✉♥③✐♦♥❡ ❞❡❧ t❡♠♣♦✱ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧❧✬❛r✐❛

♥❡❧❧✬❛♠❜✐❡♥t❡ s❡♠✐❝♦♥✜♥❛t♦ Ti✱ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡ Tmr✱ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛

❞❡❧❧❛ s✉♣❡r✜❝✐❡ ❞❡❧ ♣❛✈✐♠❡♥t♦ Tm✱ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧❧❛ s✉♣❡r✜❝✐❡ ✐♥t❡r♥❛ ❞❡❧ ✈❡tr♦ Tr,i

❡ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ❞✐ ❣❧♦❜♦t❡r♠♦♠❡tr♦ Tg ♦tt❡♥✉t✐ ❝♦♥ ❧❡ r✐❧❡✈❛③✐♦♥✐ str✉♠❡♥t❛❧✐✳

❋✐❣✉r❛ ✹✳✹✿ ❆♥❞❛♠❡♥t♦ ❞❡❧❧❡ ❣r❛♥❞❡③③❡ ♠✐s✉r❛t❡✱ ✸✵ ▲✉❣❧✐♦ ✷✵✶✷

✻✺

❙✐ ♣r♦❝❡❞❡ q✉✐♥❞✐ ❛❧ ❝♦♥❢r♦♥t♦ tr❛ ✐ r✐s✉❧t❛t✐ t❡♦r✐❝✐ ♦❣❣❡tt♦ ❞❡❧❧❛ s✐♠✉❧❛③✐♦♥❡ ❡❞ ✐ ✈❛❧♦r✐

♦tt❡♥✉t✐ ❞❛❧❧❡ ♠✐s✉r❡ str✉♠❡♥t❛❧✐✳

■♥ ❋✐❣✉r❛ ✹✳✺ ✐ ✈❛❧♦r✐ ♠✐s✉r❛t✐ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧❧❛ s✉♣❡r✜❝✐❡ ✐♥t❡r♥❛ ❞❡❧ ✈❡tr♦ ❡ ❞❡❧❧❛

t❡♠♣❡r❛t✉r❛ ❞❡❧❧❛ s✉♣❡r❢❝✐❡ ❞❡❧ ♣❛✈✐♠❡♥t♦ s♦♥♦ ❝♦♥❢r♦♥t❛t✐ ❝♦♥ ❣❧✐ ❛♥❛❧♦❣❤✐ ✈❛❧♦r✐ s✐♠✉❧❛t✐✳

❙✐ ♦ss❡r✈❛ ✐♥ ❡♥tr❛♠❜✐ ✐ ❝❛s✐ ✉♥❛ ❜✉♦♥❛ ❝♦♥❝♦r❞❛♥③❛❀ s✐ ❤❛♥♥♦ ❞✉❡ ❧✐❡✈✐ ✢❡ss✐♦♥✐ ❞❡❧ ❞❛t♦

♠✐s✉r❛t♦✱ ❝✐r❝❛ ✶✺ ♠✐♥✉t✐ ♣r✐♠❛ ❡ ✶✺ ♠✐♥✉t✐ ❞♦♣♦ ❧❡ ♦r❡ ✶✷✿✵✵✱ ❞♦✈✉t❡ ❛❧❧❛ ✐♥t❡r❝❡tt❛③✐♦♥❡

❞❛ ♣❛rt❡ ❞❡❧❧❛ t❡r♠♦❝♦♣♣✐❛ ✐♥st❛❧❧❛t❛ s✉❧❧❛ s✉♣❡r✜❝✐❡ ❞❡❧ ♣❛✈✐♠❡♥t♦ ❞❡❧❧✬♦♠❜r❡❣❣✐❛t✉r❛

❞❡❣❧✐ ❡❧❡♠❡♥t✐ ❞❡❧❧❛ str✉tt✉r❛ ♣♦rt❛♥t❡✳ ■ ❞❛t✐ s♦♥♦ ♠❡❞✐❛t✐ s✉ ✉♥ ♣❡r✐♦❞♦ ❞✐ ✺ ♠✐♥✉t✐ ♣❡r

r✐♠✉♦✈❡r❡ ❧✬❡✛❡tt♦ ❞❡❧❧❡ ✈❛r✐❛③✐♦♥✐ ❛ ❜r❡✈❡ t❡r♠✐♥❡ ❞❡✐ ♣❛r❛♠❡tr✐ ❝❧✐♠❛t✐❝✐✱ ❛❞ ❡s❡♠♣✐♦ ❧❛

✈❡❧♦❝✐tà ❞❡❧❧✬❛r✐❛ ❢♦rt❡♠❡♥t❡ ✈❛r✐❛❜✐❧❡ s♦tt♦ ❧❛ ❝♦♣❡rt✉r❛ ✭❋✐❣✉r❛ ✹✳✸ ✮✱ ❡ ♣❡r ❛tt❡♥✉❛r❡ ❧✬❡❢✲

❢❡tt♦ ❞✐ ♦♠❜r❡❣❣✐❛♠❡♥t♦ ♣❡r✐♦❞✐❝♦ ❞❡❧❧❡ s❡r✐❣r❛✜❡ s♦✈r❛♣♣♦st❡ ❛✐ ♣❛♥♥❡❧❧✐ ✐♥ ✈❡tr♦ ✭❋✐❣✉r❛

✹✳✷ ✮✳ ▲✬❛❝❝♦r❞♦ ❞❡❣❧✐ ❛♥❞❛♠❡♥t✐ ♥❡❧ t❡♠♣♦ tr❛ ✈❛❧♦r✐ s✐♠✉❧❛t✐ ❡ ♠✐s✉r❛t✐ ❞❡❧❧❡ t❡♠♣❡r❛✲

t✉r❡ s✉♣❡r✜❝✐❛❧✐ ❞❡❧ ✈❡tr♦ ❡ ❞❡❧ ♣❛✈✐♠❡♥t♦✱ è ✐♠♣♦rt❛♥t❡ ❛✐ ✜♥✐ ❞❡❧ ❝❛❧❝♦❧♦ ❝♦rr❡tt♦ ❞❡❧❧❛

t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡ ✭✷✳✹✸ ✮✱ ♣♦✐❝❤è ✐❧ ❝♦♥tr✐❜✉t♦ ❞❡❧❧♦ s❝❛♠❜✐♦ t❡r♠✐❝♦ r❛❞✐❛t✐✈♦ ❛

❜❛ss❛ ❢r❡q✉❡♥③❛ è ❢✉♥③✐♦♥❡ ❞❡❧❧❛ q✉❛rt❛ ♣♦t❡♥③❛ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ❛ss♦❧✉t❛ ❞❡❧❧❡ s✉♣❡r✜❝✐

✐rr❛❣❣✐❛♥t✐✳

❋✐❣✉r❛ ✹✳✺✿ ❈♦♥❢r♦♥t♦ tr❛ ✐ ✈❛❧♦r✐ ♠✐s✉r❛t✐ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧❧❛ s✉♣❡r✜❝✐❡ ✐♥t❡r♥❛ ❞❡❧✈❡tr♦ ❡ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧❧❛ s✉♣❡r❢❝✐❡ ❞❡❧ ♣❛✈✐♠❡♥t♦ ❝♦♥ ❣❧✐ ❛♥❛❧♦❣❤✐ ✈❛❧♦r✐ s✐♠✉❧❛t✐✱✸✵ ▲✉❣❧✐♦ ✷✵✶✷

✻✻

■♥ ❋✐❣✉r❛ ✹✳✻ s✐ r✐♣♦rt❛ ❧✬❛♥❞❛♠❡♥t♦✱ ✐♥ ❢✉♥③✐♦♥❡ ❞❡❧ t❡♠♣♦✱ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ s✐♠✉❧❛t❛

❞❡❧❧✬❛r✐❛ ♥❡❧❧♦ s♣❛③✐♦ s❡♠✐❝♦♥✜♥❛t♦ ❛❧ ❞✐ s♦tt♦ ❞❡❧❧❛ ❝♦♣❡rt✉r❛ ❡❞ ✐ ✈❛❧♦r✐ ❛♥❛❧♦❣❤✐ ♠✐s✉r❛t✐

❡ ♠❡❞✐❛t✐ s✉ ✉♥ ✐♥t❡r✈❛❧❧♦ ❞✐ ✺ ♠✐♥✉t✐✳

❋✐❣✉r❛ ✹✳✻✿ ❈♦♥❢r♦♥t♦ tr❛ t❡♠♣❡r❛t✉r❛ ❞❡❧❧✬❛r✐❛ s✐♠✉❧❛t❛ ❡ ❧✬❛♥❛❧♦❣♦ ✈❛❧♦r❡ ♠✐s✉r❛t♦✱ ✸✵▲✉❣❧✐♦ ✷✵✶✷

■♥ ❋✐❣✉r❛ ✹✳✼ s✐ r✐♣♦rt❛ ✐❧ ❝♦♥❢r♦♥t♦ tr❛ ❧❛ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡ s✐♠✉❧❛t❛ ✭✷✳✹✸ ✮

❡ ❧✬❛♥❛❧♦❣♦ ✈❛❧♦r❡ ✈❛❧✉t❛t♦ s❡❝♦♥❞♦ ❊◆ ■❙❖ ✼✼✷✻ ❬✷✸❪ ❝♦♥ ❧❛ ✭✸✳✶✼ ✮ ❛ ♣❛rt✐r❡ ❞❛✐ ✈❛❧♦r✐

♠✐s✉r❛t✐ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ❞✐ ❣❧♦❜♦t❡r♠♦♠❡tr♦✱ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ❡ ✈❡❧♦❝✐tà ❞❡❧❧✬❛r✐❛

✭❋✐❣✉r❡ ✹✳✸ ❡ ✹✳✹ ✮✳

❋✐❣✉r❛ ✹✳✼✿ ❈♦♥❢r♦♥t♦ tr❛ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡ s✐♠✉❧❛t❛ ❡ ❧✬❛♥❛❧♦❣♦ ♠✐s✉r❛t♦✱ ✸✵▲✉❣❧✐♦ ✷✵✶✷

✻✼

▲❛ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡ s✐♠✉❧❛t❛ r✐s✉❧t❛ ✐♥ s♦st❛♥③✐❛❧❡ ❛❝❝♦r❞♦ ❝♦♥ ✐ ✈❛❧♦r✐ ♠✐s✉r❛t✐✳

P❡r ❛tt❡♥✉❛r❡ ❧✬❡✛❡tt♦ ❞❡❧❧❛ ❢♦rt❡ ✈❛r✐❛❜✐❧✐tà ❞❡❧❧❛ ✈❡❧♦❝✐tà ❞❡❧❧✬❛r✐❛ ❡ ❝♦♥s✐❞❡r❛r❡ ❧✬✐♥❡r③✐❛

t❡r♠✐❝❛ ❞❡❧ ❣❧♦❜♦t❡r♠♦♠❡tr♦ ✐ ❞❛t✐ ♠✐s✉r❛t✐ s♦♥♦ st❛t✐ ♠❡❞✐❛t✐ s✉ ✐♥t❡r✈❛❧❧✐ ❞✐ ✺ ♠✐♥✉t✐✳

■❧ r✐s✉❧t❛t♦ ♦tt❡♥✉t♦ è s♦❞❞✐s❢❛❝❡♥t❡ ❛♥❝❤❡ ❝♦♥s✐❞❡r❛♥❞♦ ❝❤❡ ❧✬ ✉s♦ ❞❡❧ ❣❧♦❜♦t❡r♠♦♠❡tr♦ è

✉♥ ♠❡t♦❞♦ ❝♦♠✉♥❡ ❡ ❞✐ s❡♠♣❧✐❝❡ ❛♣♣❧✐❝❛③✐♦♥❡✱ ♠❛ ❝♦st✐t✉✐s❝❡ s♦❧♦ ✉♥✬❛♣♣r♦ss✐♠❛③✐♦♥❡ ♣❡r

❧❛ ✈❛❧✉t❛③✐♦♥❡ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡ ✭❊◆ ■❙❖ ✼✼✷✻✮✳

■♥✜♥❡✱ ♣❡r ❝❛r❛tt❡r✐③③❛r❡ ❧✬❛♠❜✐❡♥t❡ s❡♠✐❝♦♥✜♥❛t♦ ❞❛❧ ♣✉♥t♦ ❞✐ ✈✐st❛ t❡r♠✐❝♦✱ s✐ è ✉t✐❧✐③③❛t♦

❧✬✐♥❞✐❝❡ ❞✐ ❝♦♠❢♦rt t❡r♠✐❝♦ P❊❚ P❤②s✐♦❧♦❣✐❝❛❧ ❊✛❡❝t✐✈❡ ❚❡♠♣❡r❛t✉r❡ ✭❍ö♣♣❡ ❬✶✵❪✮✳ ▲✬✐♥❞✐✲

❝❡ P❊❚ è st❛t♦ ❝♦♥❝❡♣✐t♦ ❡ ✈✐❡♥❡ ✐♠♣✐❡❣❛t♦ ♣r❡✈❛❧❡♥t❡♠❡♥t❡ ♣❡r ❝❛r❛tt❡r✐③③❛r❡ ❛♠❜✐❡♥t✐

t❡r♠✐❝✐ s❡♠✐❝♦♥✜♥❛t✐ ❡❞ ❛♣❡rt✐ ♣♦✐❝❤è ♠❡tt❡ ✐♥ ❡✈✐❞❡♥③❛ ❣❧✐ ❡✛❡tt✐ ❞❡❧❧♦ s❝❛♠❜✐♦ t❡r♠✐❝♦

r❛❞✐❛t✐✈♦ tr❛ ✐❧ ❝♦r♣♦ ✉♠❛♥♦ ❡❞ ❧✬❛♠❜✐❡♥t❡ ❝✐r❝♦st❛♥t❡✳ ▲✬❡✛❡tt♦ ❞❡❧❧✬✐rr❛❣❣✐❛♠❡♥t♦ s✐❛ ❞❛

s♦r❣❡♥t❡ ❞✐ ♦♥❞❡ ❝♦rt❡ ✭✐♥ ♣❛rt✐❝♦❧❛r❡ ❞❛❧ ❙♦❧❡✮ ❝❤❡ ❞❛ s♦r❣❡♥t✐ ❞✐ ♦♥❞❡ ❧✉♥❣❤❡ ✭s✉♣❡r✜❝✐

✐♥t❡r♥❡ ❞❡❧❧✬❛♠❜✐❡♥t❡ s❡♠✐❝♦♥✜♥❛t♦✮ è s✐♥t❡t✐③③❛t♦ ♥❡❧❧❛ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡ ❞❡❧✲

❧✬❛♠❜✐❡♥t❡ ❝❤❡ r✐❡♥tr❛ ❛❧❧✬✐♥t❡r♥♦ ❞❡❧ ❝❛❧❝♦❧♦ ❞❡❧❧✬✐♥❞✐❝❡ P❊❚ ✐♠♣❧❡♠❡♥t❛t♦ ♥❡❧ s♦❢t✇❛r❡

❘❛②▼❛♥ ✶✳✷ ❬✷✵❪✳ P❡rt❛♥t♦ ✉♥♦ ❞❡✐ ♣✐ù ✐♠♣♦rt❛♥t✐ ❢❛tt♦r✐ ❝❤❡ ❝♦♥❝♦rr♦♥♦ ❛❧❧❛ ❝❛r❛tt❡✲

r✐③③❛③✐♦♥❡ ❞✐ ✉♥ ❛♠❜✐❡♥t❡ ❞❛❧ ♣✉♥t♦ ❞✐ ✈✐st❛ t❡r♠✐❝♦ è ❧❛ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡✳

■♥ ❋✐❣✉r❛ ✹✳✽ s✐ r✐♣♦rt❛♥♦ ❧✬✐♥❞✐❝❡ P❊❚ ❡ ❧❛ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡ ✐♥ ❢✉♥③✐♦♥❡ ❞❡❧

t❡♠♣♦✳

❋✐❣✉r❛ ✹✳✽✿ P❊❚ ❡ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡ ❝❛❧❝♦❧❛t✐ ♦❣♥✐ 15 s✱ ✸✵ ▲✉❣❧✐♦ ✷✵✶✷

✻✽

◆❡❧ ❣r❛✜❝♦ ❞✐ ❋✐❣✉r❛ ✹✳✽ ❧❛ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡ ❡ ❧✬✐♥❞✐❝❡ P❊❚ s♦♥♦ ❝❛❧❝♦❧❛t✐ ❛

♣❛rt✐r❡ ❞❛✐ ❞❛t✐ ❛❝q✉✐s✐t✐ ♦❣♥✐ 15 s ❞❛❧❧❛ ❧❛ ❝❡♥tr❛❧✐♥❛ ♠✐❝r♦❝❧✐♠❛t✐❝❛ ❉❡❧t❛❖❍▼ ❍❉✸✷✳✶✱

q✉❡st♦ ♣❡r♠❡tt❡ ❞✐ ♠❡tt❡r❡ ✐♥ ❡✈✐❞❡♥③❛ ❧❛ ❢♦rt❡ ❞✐♣❡♥❞❡♥③❛ ❞❡❧❧✬✐♥❞✐❝❡ ❞✐ ❝♦♠❢♦rt t❡r♠✐❝♦

❞❛❧❧❛ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡ ❞❡❧❧✬❛♠❜✐❡♥t❡✳ ■♥ ❚❛❜❡❧❧❛ ✹✳✸ s✐ r✐♣♦rt❛♥♦ ✐ ✈❛❧♦r✐ ♠❡❞✐

♦r❛r✐ ❞❡✐ ♣❛r❛♠❡tr✐ ♠✐❝r♦❝❧✐♠❛t✐❝✐ r✐❧❡✈❛t✐ ❞❛❧❧❛ ❧❛ ❝❡♥tr❛❧✐♥❛ ❝❤❡ ❝♦♥❝♦rr♦♥♦ ❛❧❧❛ ❝❛r❛tt❡✲

r✐③③❛③✐♦♥❡ ❞❡❧❧✬❛♠❜✐❡♥t❡ t❡r♠✐❝♦ s❡♠✐❝♦♥✜♥❛t♦ ❡❞ ✐ ❝♦rr✐s♣♦♥❞❡♥t✐ ✈❛❧♦r✐ ❞❡❧❧✬✐♥❞✐❝❡ P❊❚

✭✐♥ ❚❛❜❡❧❧❛ ✷✳✺ è r✐♣♦rt❛t❛ ❧❛ ❝♦rr❡❧❛③✐♦♥❡ tr❛ ♣❡r❝❡③✐♦♥❡ ❞❡❧❧✬❛♠❜✐❡♥t❡ t❡r♠✐❝♦ ❡❞ ✐♥❞✐❝❡

P❊❚ ✮✳

Ora Ta (◦C) UR (%) Va (m/s) Tmr (◦C) PET (◦C)

✶✶ 29.3 51.2 1.0 51.5 38

✶✷ 30.6 47.1 0.93 53.5 40.2

✶✸ 31.5 44.9 1.1 53.9 40.7

✶✹ 32.8 40.7 0.94 55.1 42.6

❚❛❜❡❧❧❛ ✹✳✸✿ P❛r❛♠❡tr✐ ♠✐❝r♦❝❧✐♠❛t✐❝✐ r✐❧❡✈❛t✐ ♥❡❧❧✬❛♠❜✐❡♥t❡ s❡♠✐❝♦♥✜♥❛t♦ ❡❞ ✐♥❞✐❝❡ P❊❚✱♠❡❞✐❡ ♦r❛r✐❡✱ ✸✵ ▲✉❣❧✐♦ ✷✵✶✷

✻✾

✹✳✷ ●✐♦r♥♦ ✷✻ ▼❛r③♦ ✷✵✶✷

▲❡ r✐❧❡✈❛③✐♦♥✐ s♣❡r✐♠❡♥t❛❧✐ ❞❡✐ ❞❛t✐ ♠✐❝r♦❝❧✐♠❛t✐❝✐ r✐❣✉❛r❞❛♥♦ ✐❧ ❣✐♦r♥♦ 26 Marzo 2012 tr❛

❧❡ ♦r❡ 11 : 10 ❡ ❧❡ ♦r❡ 14 : 00 ✭♦r❛ s♦❧❛r❡✮✳ ■♥ ❋✐❣✉r❛ ✹✳✾ s✐ r✐♣♦rt❛ ❧✬❛♥❞❛♠❡♥t♦✱ ✐♥ ❢✉♥③✐♦♥❡

❞❡❧ t❡♠♣♦✱ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ❡st❡r♥❛✱ ❡❧❛❜♦r❛t❛ ❡ s❝♦♠♣♦st❛✱ ❛♣♣❧✐❝❛♥❞♦ ❧❡ ❡q✉❛③✐♦♥✐

♠♦str❛t❡ ♥❡❧ ♣❛r❛❣r❛❢♦ ✷✳✹✳✸ ❈❛❧❝♦❧✐ s✉❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡✱ ♥❡❧❧❡ ❝♦♠♣♦♥❡♥t✐ ❞✐r❡tt❛ ❡

❞✐✛✉s❛✳ ■❧ ❞❛t♦ ✐♥✐③✐❛❧❡ ❞✐ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ t♦t❛❧❡ s✉ ♣✐❛♥♦ ♦r✐③③♦♥t❛❧❡ è ✐❧ ✈❛❧♦r❡ ♠❡❞✐♦

♦r❛r✐♦ r✐❧❡✈❛t♦ ❞❛ ❆❘P❆ ♣r❡ss♦ ❧❛ st❛③✐♦♥❡ ♠❡t❡r❡♦❧♦❣✐❝❛ ✉r❜❛♥❛✳ ◗✉❡st✐ ❞❛t✐ r❡❧❛t✐✈✐ ❛❧❧❛

r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ❡st❡r♥❛✱ ❡❧❛❜♦r❛t✐ ♣❡r t❡♥❡r ❝♦♥t♦ ❞❡❧❧✬✐♥❝❧✐♥❛③✐♦♥❡ β ❞❡❧❧❛ s✉♣❡r✜❝✐❡ ❞❡❧❧❛

❝♦♣❡rt✉r❛✱ ✉♥✐t❛♠❡♥t❡ ❛✐ ✈❛❧♦r✐ ❝❛❧❝♦❧❛t✐ ❞❡❧❧✬❛♥❣♦❧♦ ❞✐ ✐♥❝✐❞❡♥③❛ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡✱

❝♦♥❝♦rr♦♥♦ ❛❧❧❛ ❞❡✜♥✐③✐♦♥❡ ❞❡❧❧❡ ❝♦♥❞✐③✐♦♥✐ ❛❧ ❝♦♥t♦r♥♦ ❞❡❧ ♠♦❞❡❧❧♦ ❞✐ ❝❛❧❝♦❧♦✳

❋✐❣✉r❛ ✹✳✾✿ ❘❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ❡st❡r♥❛ ❞✐r❡tt❛ ❡ ❞✐✛✉s❛✱ ✷✻ ▼❛r③♦ ✷✵✶✷

■♥ ❋✐❣✉r❛ ✹✳✶✵ s✐ r✐♣♦rt❛ ❧✬❛♥❞❛♠❡♥t♦✱ ✐♥ ❢✉♥③✐♦♥❡ ❞❡❧ t❡♠♣♦✱ ❞❡❧❧❛ ✈❡❧♦❝✐tà ❞❡❧❧✬❛r✐❛ ♠✐✲

s✉r❛t❛ s♦tt♦ ❧❛ ❝♦♣❡rt✉r❛✱ ♥❡❝❡ss❛r✐❛ ♣❡r ✐❧ ❝❛❧❝♦❧♦ ❞❡✐ ❝♦❡✣❝✐❡♥t✐ ❞✐ s❝❛♠❜✐♦ t❡r♠✐❝♦

❝♦♥✈❡tt✐✈♦ ❡ ♣❡r ❧✬❛♥❛❧✐s✐ ❞❡❧❧❡ ❝♦♥❞✐③✐♦♥✐ ❞✐ ❝♦♠❢♦rt t❡r♠✐❝♦ ♥❡❧❧✬❛♠❜✐❡♥t❡ s❡♠✐❝♦♥✜♥❛t♦✳

✼✵

❋✐❣✉r❛ ✹✳✶✵✿ ❱❡❧♦❝✐tà ❞❡❧❧✬❛r✐❛ ♠✐s✉r❛t❛ s♦tt♦ ❧❛ ❝♦♣❡rt✉r❛✱ ✷✻ ▼❛r③♦ ✷✵✶✷

■♥ ❚❛❜❡❧❧❛ ✹✳✹ s✐ r✐♣♦rt❛♥♦ ✐ ❞❛t✐ ❝❧✐♠❛t✐❝✐ ♠❡❞✐ ♦r❛r✐ r✐❧❡✈❛t✐ ❞❛ ❆❘P❆ ♣r❡ss♦ ❧❛

st❛③✐♦♥❡ ♠❡t❡r❡♦❧♦❣✐❝❛ ✉r❜❛♥❛ ❝❤❡ ❝♦♠♣❧❡t❛♥♦ ❧❡ ❝♦♥❞✐③✐♦♥✐ ❛❧ ❝♦♥t♦r♥♦ ❞❡❧ ♠♦❞❡❧❧♦ ❞✐

❝❛❧❝♦❧♦✿ t❡♠♣❡r❛t✉r❛ ❞❡❧❧✬❛r✐❛ ❡st❡r♥❛ Te✱ ✉♠✐❞✐tà r❡❧❛t✐✈❛ ❡st❡r♥❛ UR✱ ✈❡❧♦❝✐tà ❞❡❧ ✈❡♥t♦

❡st❡r♥♦ Va✳ ■♥♦❧tr❡ s❡♠♣r❡ ✐♥ ❚❛❜❡❧❧❛ ✹✳✹ s✐ r✐♣♦rt❛ ❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧❧❛ ✈♦❧t❡ ❝❡❧❡st❡

❛❧❧✬✐♥✜♥✐t♦ Tsky ♦tt❡♥✉t❛ ❞❛❧❧❛ r❛❝❝♦❧t❛ ❞✐ ❞❛t✐ ❝❧✐♠❛t✐❝✐ ▼❡t❡♦♥♦r♠✳

Ora Te (◦C) UR (%) Va (m/s) Tsky (◦C)

11 17.8 40 1.3 −1.73

12 19.9 31 1 0.85

13 21.3 27 0.8 1.81

14 21.8 26 0.7 1.03

15 23.2 23 0 2.17

❚❛❜❡❧❧❛ ✹✳✹✿ ❉❛t✐ ❝❧✐♠❛t✐❝✐ ♠❡❞✐ ♦r❛r✐ r✐❧❡✈❛t✐ ❞❛ ❆❘P❆ ❡ t❡♠♣❡r❛t✉r❛ ❞❡❧❧❛ ✈♦❧t❛ ❝❡❧❡st❡❛❧❧✬✐♥✜♥✐t♦ ❞❛ ▼❡t❡♦♥♦r♠✱ ✷✻ ▼❛r③♦ ✷✵✶✷

▲❛ s♦❧✉③✐♦♥❡ ♥✉♠❡r✐❝❛ ❞❡❧ ♠♦❞❡❧❧♦✱ ✐♥ ♣❛rt✐❝♦❧❛r❡ ❧✬✐♥t❡❣r❛③✐♦♥❡ ❞❡❧❧❡ ❡q✉❛③✐♦♥✐ ✭✷✳✶ ✮✱

✭✷✳✼ ✮ ❡ ✭✷✳✽ ✮ ❝♦♥ ❧❡ r❡❧❛t✐✈❡ ❝♦♥❞✐③✐♦♥✐ ❛❧ ❝♦♥t♦r♥♦✱ ❡❞ ✐❧ ❝❛❧❝♦❧♦✱ ✐♥ ❢✉♥③✐♦♥❡ ❞❡❧ t❡♠♣♦✱

❞❡✐ ♣❛r❛♠❡tr✐ ♠✐❝r♦❝❧✐♠❛t✐❝✐ ❞✐ ✐♥t❡r❡ss❡ ♣❡r ❧❛ ❝❛r❛tt❡r✐③③❛③✐♦♥❡ ❞❡❧❧✬❛♠❜✐❡♥t❡ t❡r♠✐❝♦

s❡♠✐❝♦♥✜♥❛t♦✱ s♦♥♦ ❛✣❞❛t✐ ❛❞ ✉♥ ❝♦❞✐❝❡ ❞✐ ❝❛❧❝♦❧♦ s✈✐❧✉♣♣❛t♦ ✐♥ ❛♠❜✐❡♥t❡ ▼❛t❧❛❜✳ ▲❡

❝♦♥❞✐③✐♦♥✐ ✐♥✐③✐❛❧✐ ❛ss✉♥t❡✱ r✐♣♦rt❛t❡ ✐♥ ❚❛❜❡❧❧❛ ✹✳✺✱ s♦♥♦ ❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧❧✬❛r✐❛ Ti ♥❡❧❧♦

s♣❛③✐♦ s❡♠✐❝♦♥✜♥❛t♦✱ ❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧❧❛ s✉♣❡r✜❝✐❡ ✐♥t❡r♥❛ ❞❡❧❧❛ ❝♦♣❡rt✉r❛ Tr,i ❡ ❧❛ t❡♠✲

✼✶

♣❡r❛t✉r❛ ❞❡❧❧❛ s✉♣❡r✜❝✐❡ ❞❡❧ ♣❛✈✐♠❡♥t♦ Tm ♦tt❡♥✉t❡ ❞❛❧❧❡ r✐❧❡✈❛③✐♦♥✐ str✉♠❡♥t❛❧✐ ❛❧❧❡ ♦r❡

11 : 10✳

Ti (◦C) Tr,i (

◦C) Tm (◦C)

18 34.53 22.58

❚❛❜❡❧❧❛ ✹✳✺✿ ❈♦♥❞✐③✐♦♥✐ ✐♥✐③✐❛❧✐ ❞❡❧ ♠♦❞❡❧❧♦✱ ✷✻ ▼❛r③♦ ✷✵✶✷

■♥ ❋✐❣✉r❛ ✹✳✶✶ s✐ r✐♣♦rt❛♥♦ ❣❧✐ ❛♥❞❛♠❡♥t✐✱ ✐♥ ❢✉♥③✐♦♥❡ ❞❡❧ t❡♠♣♦✱ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧❧✬❛✲

r✐❛ ♥❡❧❧✬❛♠❜✐❡♥t❡ s❡♠✐❝♦♥✜♥❛t♦ Ti✱ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡ Tmr✱ ❞❡❧❧❛ t❡♠♣❡r❛✲

t✉r❛ ❞❡❧❧❛ s✉♣❡r✜❝✐❡ ❞❡❧ ♣❛✈✐♠❡♥t♦ Tm✱ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧❧❛ s✉♣❡r✜❝✐❡ ✐♥t❡r♥❛ ❞❡❧ ✈❡tr♦

Tr,i ❡ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ❞✐ ❣❧♦❜♦t❡r♠♦♠❡tr♦ Tg ♦tt❡♥✉t✐ ❝♦♥ ❧❡ r✐❧❡✈❛③✐♦♥✐ str✉♠❡♥t❛❧✐✳

❋✐❣✉r❛ ✹✳✶✶✿ ❆♥❞❛♠❡♥t♦ ❞❡❧❧❡ ❣r❛♥❞❡③③❡ ♠✐s✉r❛t❡✱ ✷✻ ▼❛r③♦ ✷✵✶✷

■♥ ❋✐❣✉r❛ ✹✳✶✶ s✐ ♥♦t❛ ❧✬❛ss❡♥③❛ ❞✐ ❞❛t✐ r✐❧❡✈❛t✐ ♣❡r q✉❛♥t♦ r✐❣✉❛r❞❛ ❧❛ t❡♠♣❡r❛t✉r❛ ❞✐

❣❧♦❜♦t❡r♠♦♠❡tr♦ Tg ❡ ❧❛ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡ Tmr ♥❡❣❧✐ ✐♥t❡r✈❛❧❧✐ 11 : 40− 12 : 15✱

12 : 40 − 13 : 15 ❡ 13 : 40 − 14 : 00✱ ♣♦✐❝❤è ✐♥ q✉❡st✐ ♣❡r✐♦❞✐ ❞✐ t❡♠♣♦ s✐ s♦♥♦ ❡✛❡tt✉❛t❡

♠✐s✉r❛③✐♦♥✐ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡ ❞❡❧❧✬❛♠❜✐❡♥t❡ ❡st❡r♥♦ ❛❧❧❛ ❝♦♣❡rt✉r❛ s♣♦✲

st❛♥❞♦ ❧❛ ❝❡♥tr❛❧✐♥❛ ♠✐❝r♦❝❧✐♠❛t✐❝❛✳ ❚r❛ ❧❡ ♦r❡ 13 : 00 ❡ ❧❡ ♦r❡ 13 : 25 ✐❧ ❞❛t♦ r❡❧❛t✐✈♦ ❛❧❧❛

✼✷

t❡♠♣❡r❛t✉r❛ ❞❡❧❧❛ s✉♣❡r✜❝✐❡ ❞❡❧ ♣❛✈✐♠❡♥t♦ Tm ❡ ❞❡❧❧❛ s✉♣❡r✜❝✐❡ ✐♥t❡r♥❛ ❞❡❧ ✈❡tr♦ Tr,i✱ ♥♦♥

è st❛t♦ ❛❝q✉✐s✐t♦ ♣❡r ♣r♦❜❧❡♠✐ t❡❝♥✐❝✐✳

❙✐ ♣r♦❝❡❞❡ q✉✐♥❞✐ ❛❧ ❝♦♥❢r♦♥t♦ tr❛ ✐ r✐s✉❧t❛t✐ t❡♦r✐❝✐ ♦❣❣❡tt♦ ❞❡❧❧❛ s✐♠✉❧❛③✐♦♥❡ ❡❞ ✐ ✈❛❧♦✲

r✐ ♦tt❡♥✉t✐ ❞❛❧❧❡ ♠✐s✉r❡ str✉♠❡♥t❛❧✐✳ ■♥ ❋✐❣✉r❛ ✹✳✶✷ ✐ ✈❛❧♦r✐ ♠✐s✉r❛t✐ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛

❞❡❧❧❛ s✉♣❡r✜❝✐❡ ✐♥t❡r♥❛ ❞❡❧ ✈❡tr♦ ❡ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧❧❛ s✉♣❡r❢❝✐❡ ❞❡❧ ♣❛✈✐♠❡♥t♦ s♦♥♦

❝♦♥❢r♦♥t❛t✐ ❝♦♥ ❣❧✐ ❛♥❛❧♦❣❤✐ ✈❛❧♦r✐ s✐♠✉❧❛t✐✳ ❙✐ ♦ss❡r✈❛ ✐♥ ❡♥tr❛♠❜✐ ✐ ❝❛s✐ ✉♥❛ s✉✣❝✐❡♥t❡

❝♦♥❝♦r❞❛♥③❛ ❝♦♥s✐❞❡r❛♥❞♦ ❝❤❡ ✐ ❞❛t✐ r❡❧❛t✐✈✐ ❛❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ♥♦♥ s♦♥♦ st❛t✐ ♠✐s✉r❛t✐

✐♥ ❧♦❝♦✱ ♠❛ s✐ tr❛tt❛ ❞✐ ✈❛❧♦r✐ ♠❡❞✐ ♦r❛r✐ ❢♦r♥✐t✐ ❞❛ ❆❘P❆ ❝♦♠❡ ♣r❡❝❡❞❡♥t❡♠❡♥t❡ ❡✈✐❞❡♥✲

③✐❛t♦✳ ❙✐ ♦ss❡r✈❛♥♦ tr❡ ✢❡ss✐♦♥✐ ❞❡❧ ❞❛t♦ ♠✐s✉r❛t♦✱ r❡❧❛t✐✈♦ ❛❧❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧ ♣❛✈✐♠❡♥t♦✱

r✐s♣❡tt♦ ❛❧ ✈❛❧♦r❡ s✐♠✉❧❛t♦✱ ❞♦✈✉t❡ ❛❧❧✬✐♥t❡r❝❡tt❛③✐♦♥❡ ❞❛ ♣❛rt❡ ❞❡❧❧❛ t❡r♠♦❝♦♣♣✐❛ ✐♥st❛❧❧❛t❛

s✉❧❧❛ s✉♣❡r✜❝✐❡ ❞❡❧ ♣❛✈✐♠❡♥t♦ ❞❡❧❧✬♦♠❜r❡❣❣✐❛t✉r❛ ❞❡❣❧✐ ❡❧❡♠❡♥t✐ ❞❡❧❧❛ str✉tt✉r❛ ♣♦rt❛♥t❡✳

■ ❞❛t✐ s♦♥♦ ♠❡❞✐❛t✐ s✉ ✉♥ ♣❡r✐♦❞♦ ❞✐ ✺ ♠✐♥✉t✐ ♣❡r r✐♠✉♦✈❡r❡ ❧✬❡✛❡tt♦ ❞❡❧❧❡ ✈❛r✐❛③✐♦♥✐ ❛

❜r❡✈❡ t❡r♠✐♥❡ ❞❡✐ ♣❛r❛♠❡tr✐ ❝❧✐♠❛t✐❝✐✱ ❛❞ ❡s❡♠♣✐♦ ❧❛ ✈❡❧♦❝✐tà ❞❡❧❧✬❛r✐❛ ❢♦rt❡♠❡♥t❡ ✈❛r✐❛❜✐❧❡

s♦tt♦ ❧❛ ❝♦♣❡rt✉r❛ ✭❋✐❣✉r❛ ✹✳✶✵✮✱ ❡ ♣❡r ❛tt❡♥✉❛r❡ ❧✬❡✛❡tt♦ ❞✐ ♦♠❜r❡❣❣✐❛♠❡♥t♦ ♣❡r✐♦❞✐❝♦

❞❡❧❧❡ s❡r✐❣r❛✜❡ s♦✈r❛♣♣♦st❡ ❛✐ ♣❛♥♥❡❧❧✐ ✐♥ ✈❡tr♦✳

❋✐❣✉r❛ ✹✳✶✷✿ ❈♦♥❢r♦♥t♦ tr❛ ✐ ✈❛❧♦r✐ ♠✐s✉r❛t✐ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧❧❛ s✉♣❡r✜❝✐❡ ✐♥t❡r♥❛ ❞❡❧✈❡tr♦ ❡ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧❧❛ s✉♣❡r❢❝✐❡ ❞❡❧ ♣❛✈✐♠❡♥t♦ ❝♦♥ ❣❧✐ ❛♥❛❧♦❣❤✐ ✈❛❧♦r✐ s✐♠✉❧❛t✐✱✷✻ ▼❛r③♦ ✷✵✶✷

✼✸

■♥ ❋✐❣✉r❛ ✹✳✶✸ s✐ r✐♣♦rt❛ ❧✬❛♥❞❛♠❡♥t♦✱ ✐♥ ❢✉♥③✐♦♥❡ ❞❡❧ t❡♠♣♦✱ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ s✐♠✉❧❛t❛

❞❡❧❧✬❛r✐❛ ♥❡❧❧♦ s♣❛③✐♦ s❡♠✐❝♦♥✜♥❛t♦ ❛❧ ❞✐ s♦tt♦ ❞❡❧❧❛ ❝♦♣❡rt✉r❛ ❡❞ ✐ ✈❛❧♦r✐ ❛♥❛❧♦❣❤✐ ♠✐s✉r❛t✐

❡ ♠❡❞✐❛t✐ s✉ ✉♥ ✐♥t❡r✈❛❧❧♦ ❞✐ ✺ ♠✐♥✉t✐✳

❋✐❣✉r❛ ✹✳✶✸✿ ❈♦♥❢r♦♥t♦ tr❛ t❡♠♣❡r❛t✉r❛ ❞❡❧❧✬❛r✐❛ s✐♠✉❧❛t❛ ❡ ❧✬❛♥❛❧♦❣♦ ♠✐s✉r❛t♦✱ ✷✻ ▼❛r③♦✷✵✶✷

■♥ ❋✐❣✉r❛ ✹✳✶✹ s✐ r✐♣♦rt❛ ✐❧ ❝♦♥❢r♦♥t♦ tr❛ ❧❛ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡ s✐♠✉❧❛t❛ ✭✷✳✹✸ ✮ ❡

❧✬❛♥❛❧♦❣♦ ✈❛❧♦r❡ ✈❛❧✉t❛t♦ s❡❝♦♥❞♦ ❊◆ ■❙❖ ✼✼✷✻ ❝♦♥ ❧❛ ✭✸✳✶✼ ✮ ❛ ♣❛rt✐r❡ ❞❛✐ ✈❛❧♦r✐ ♠✐s✉r❛t✐

❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ❞✐ ❣❧♦❜♦t❡r♠♦♠❡tr♦✱ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ❡ ✈❡❧♦❝✐tà ❞❡❧❧✬❛r✐❛ ✭❋✐❣✉r❡ ✹✳✶✵

❡ ❡ ✹✳✶✶ ✮✳

❋✐❣✉r❛ ✹✳✶✹✿ ❈♦♥❢r♦♥t♦ tr❛ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡ s✐♠✉❧❛t❛ ❡ ❧✬❛♥❛❧♦❣♦ ✈❛❧♦r❡♠✐s✉r❛t♦✱ ✷✻ ▼❛r③♦ ✷✵✶✷

✼✹

▲❛ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡ s✐♠✉❧❛t❛ r✐s✉❧t❛ ✐♥ s♦st❛♥③✐❛❧❡ ❛❝❝♦r❞♦ ❝♦♥ ✐ ✈❛❧♦r✐ ♠✐s✉r❛t✐✳

P❡r ❛tt❡♥✉❛r❡ ❧✬❡✛❡tt♦ ❞❡❧❧❛ ❢♦rt❡ ✈❛r✐❛❜✐❧✐tà ❞❡❧❧❛ ✈❡❧♦❝✐tà ❞❡❧❧✬❛r✐❛ ❡ ❝♦♥s✐❞❡r❛r❡ ❧✬✐♥❡r③✐❛

t❡r♠✐❝❛ ❞❡❧ ❣❧♦❜♦t❡r♠♦♠❡tr♦ ✐ ❞❛t✐ ♠✐s✉r❛t✐ s♦♥♦ st❛t✐ ♠❡❞✐❛t✐ s✉ ✐♥t❡r✈❛❧❧✐ ❞✐ ✺ ♠✐♥✉t✐✳ ■♥

❋✐❣✉r❛ ✹✳✶✹ s✐ ♥♦t❛ ❧✬❛ss❡♥③❛ ❞✐ ❞❛t✐ r✐❧❡✈❛t✐ ♥❡❣❧✐ ✐♥t❡r✈❛❧❧✐ 11 : 40−12 : 15✱ 12 : 40−13 : 15

❡ 13 : 40 − 14 : 00✱ ♣♦✐❝❤è ✐♥ q✉❡st✐ ♣❡r✐♦❞✐ ❞✐ t❡♠♣♦ s✐ s♦♥♦ ❡✛❡tt✉❛t❡ ♠✐s✉r❛③✐♦♥✐ ❞❡❧❧❛

t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡ ❞❡❧❧✬❛♠❜✐❡♥t❡ ❡st❡r♥♦ ❛❧❧❛ ❝♦♣❡rt✉r❛ ❝♦♠❡ ❣✐à ♦ss❡r✈❛t♦✳

■♥✜♥❡✱ ♣❡r ❝❛r❛tt❡r✐③③❛r❡ ❧✬❛♠❜✐❡♥t❡ s❡♠✐❝♦♥✜♥❛t♦ ❞❛❧ ♣✉♥t♦ ❞✐ ✈✐st❛ t❡r♠✐❝♦✱ s✐ è ✉t✐❧✐③③❛t♦

❧✬✐♥❞✐❝❡ ❞✐ ❝♦♠❢♦rt t❡r♠✐❝♦ P❊❚ ✳ ■♥ ❋✐❣✉r❛ ✹✳✶✺ s✐ r✐♣♦rt❛♥♦ ❧✬✐♥❞✐❝❡ P❊❚ ❡ ❧❛ t❡♠♣❡r❛t✉r❛

♠❡❞✐❛ r❛❞✐❛♥t❡ ✐♥ ❢✉♥③✐♦♥❡ ❞❡❧ t❡♠♣♦✳

❋✐❣✉r❛ ✹✳✶✺✿ P❊❚ ❡ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡ ♥❡❧❧✬❛♠❜✐❡♥t❡ s❡♠✐❝♦♥✜♥❛t♦ ❝❛❧❝♦❧❛t✐ ♦❣♥✐15 s✱ ✷✻ ▼❛r③♦ ✷✵✶✷

❋✐❣✉r❛ ✹✳✶✻✿ P❊❚ ❡ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡ ♥❡❧❧✬❛♠❜✐❡♥t❡ ❡st❡r♥♦ ❝❛❧❝♦❧❛t✐ ♦❣♥✐ 15 s✱✷✻ ▼❛r③♦ ✷✵✶✷

✼✺

■♥ r✐❢❡r✐♠❡♥t♦ ❛❧❧❡ ♠✐s✉r❡ ❡✛❡tt✉❛t❡ ❛❧❧✬❡st❡r♥♦ ❞❡❧❧❛ ❝♦♣❡rt✉r❛ ♠❡❞✐❛♥t❡ ❧♦ s♣♦st❛♠❡♥t♦

❞❡❧❧❛ ❝❡♥tr❛❧✐♥❛ ♠✐❝r♦❝❧✐♠❛t✐❝❛ ♥❡❣❧✐ ✐♥t❡r✈❛❧❧✐ ♦r❛r✐ 11 : 40 − 12 : 15✱ 12 : 40 − 13 : 15 ❡

13 : 40 − 14 : 00 s✐ r✐♣♦rt❛ ❧✬❛♥❞❛♠❡♥t♦ ❞❡❧❧❛ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡ ❡ ❞❡❧❧✬✐♥❞✐❝❡ ❞✐

❝♦♠❢♦rt t❡r♠✐❝♦ P❊❚ ✐♥ ❢✉♥③✐♦♥❡ ❞❡❧ t❡♠♣♦ ✭❋✐❣✉r❛ ✹✳✶✻ ✮✳

❈♦♥❢r♦♥t❛♥❞♦ ✐ ❞✉❡ ❣r❛✜❝✐ ❞✐ ❋✐❣✉r❡ ✹✳✶✺ ❡ ✹✳✶✻✱ s✐ ♥♦t❛ ✉♥ ❛✉♠❡♥t♦ ❞❡❧❧✬♦r❞✐♥❡ ❞✐ ❞✐❡❝✐

❣r❛❞✐ ❈❡❧s✐✉s ❞❡❧❧✬✐♥❞✐❝❡ P❊❚ ♣❛ss❛♥❞♦ ❞❛❧❧✬❛♠❜✐❡♥t❡ s❡♠✐❝♦♥✜♥❛t♦ ❛❧❧✬❛♠❜✐❡♥t❡ ❡st❡r♥♦✱

♣♦✐❝❤è ❧❛ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡ è s❡♥s✐❜✐❧♠❡♥t❡ ♣✐ù ❛❧t❛ ♥♦♥ ❡ss❡♥❞♦✈✐ ❧✬❡✛❡tt♦

s❝❤❡r♠❛♥t❡ ❞❡❧❧❛ ❝♦♣❡rt✉r❛✳ ❙❡❝♦♥❞♦ ❧❛ s❝❛❧❛ ❞❡❧❧✬✐♥❞✐❝❡ P❊❚✱ r✐♣♦rt❛t❛ ✐♥ ❚❛❜❡❧❧❛ ✷✳✺✱

s✐ ♦ss❡r✈❛ ❝❤❡ ❧❛ ♣❡r❝❡③✐♦♥❡ ❞❡❧❧✬❛♠❜✐❡♥t❡ t❡r♠✐❝♦ s♦tt♦ ❧❛ ❝♦♣❡rt✉r❛ r✐❡♥tr❛ ♥❡❧❧❛ ❢❛s❝✐❛

❝♦♠❢♦rt✲❧❡❣❣❡r♠❡♥t❡ t✐❡♣✐❞♦✱ ♠❡♥tr❡ ❛❧❧✬❡st❡r♥♦ ❞❡❧❧❛ ❝♦♣❡rt✉r❛ ❧❡ ❝♦♥❞✐③✐♦♥✐ t❡r♠✐❝❤❡ s♦♥♦

t❡♥❞❡♥t✐ ❛❧❧❛ ❢❛s❝✐❛ ❝❛❧❞♦✳

✼✻

✺ ❈♦♥❝❧✉s✐♦♥✐

◆❡❧ ♣r❡s❡♥t❡ ❧❛✈♦r♦ ❞✐ t❡s✐ s✐ è ❡✛❡tt✉❛t❛ ❧❛ ✈❡r✐✜❝❛ s♣❡r✐♠❡♥t❛❧❡ ❞❡❧ ♠♦❞❡❧❧♦ ❞✐ ❝❛❧❝♦❧♦

❡ ❞❡❧❧❡ ❛ss✉♥③✐♦♥✐ ✐♠♣✐❡❣❛t❡ ♣❡r ❧❛ ♣r❡✈✐s✐♦♥❡ ❞❡❧ ❝♦♠♣♦rt❛♠❡♥t♦ t❡r♠✐❝♦ ❞❡❧❧✬❛♠❜✐❡♥t❡

s❡♠✐❝♦♥✜♥❛t♦ ❞❛❧❧❛ ♥✉♦✈❛ ❝♦♣❡rt✉r❛ ✐♥ ✈❡tr♦ r❡❛❧✐③③❛t❛ ✐♥ ♣✐❛③③❛ ●❤✐❛✐❛ ❛ P❛r♠❛✳ ■♥♦❧tr❡

s✐ è ♣r♦❝❡❞✉t♦ ❛❧❧✬❛♥❛❧✐s✐ ❞❡❧❧❡ ❝♦♥❞✐③✐♦♥✐ ❞✐ ❝♦♠❢♦rt t❡r♠✐❝♦ ✐♠♣✐❡❣❛♥❞♦ ❧✬✐♥❞✐❝❡ P❊❚

P❤②s✐♦❧♦❣✐❝❛❧ ❊✛❡❝t✐✈❡ ❚❡♠♣❡r❛t✉r❡ ❜❛s❛t♦ s✉❧ ♠♦❞❡❧❧♦ ❞✐ t❡r♠♦r❡❣♦❧❛③✐♦♥❡ ❝♦r♣♦r❡❛ ❛

❞✉❡ ♥♦❞✐ ▼❊▼■ ▼✉♥✐❝❤ ❊♥❡r❣② ❜❛❧❛♥❝❡ ▼♦❞❡❧ ❢♦r ■♥❞✐✈✐❞✉❛❧s✳

P❡r ❧❛ ✈❛❧✐❞❛③✐♦♥❡ ❞❡❧ ♠♦❞❡❧❧♦ è st❛t❛ ❝♦♥❞♦tt❛ ✉♥❛ ❝❛♠♣❛❣♥❛ ❞✐ ♠✐s✉r❡ ❛❧ ❞✐ s♦tt♦ ❡❞

❛❧❧✬❡st❡r♥♦ ❞❡❧❧❛ ❝♦♣❡rt✉r❛ ♣❡r ✈❛❧✉t❛r❡ ❧❡ ❣r❛♥❞❡③③❡ ❝❤❡ ❝♦st✐t✉✐s❝♦♥♦ ❧❡ ❝♦♥❞✐③✐♦♥✐ ❛❧

❝♦♥t♦r♥♦ ❞❡❧ ♠♦❞❡❧❧♦ st❡ss♦ ❡ ♣❡r st✐♠❛r❡ ✐ ♣❛r❛♠❡tr✐ ♠✐❝r♦❝❧✐♠❛t✐❝✐ ❝❤❡ ❝♦♥❝♦rr♦♥♦ ❛❧❧❛

❝❛r❛tt❡r✐③③❛③✐♦♥❡ ❞❡❧❧✬❛♠❜✐❡♥t❡ t❡r♠✐❝♦✳ ■❧ ❝♦♥❢r♦♥t♦ tr❛ ✐ r✐s✉❧t❛t✐ ❞❡❧❧❡ s✐♠✉❧❛③✐♦♥✐✱ ❝♦♥✲

t❡st✉❛❧✐③③❛t❡ ♥❡✐ ❣✐♦r♥✐ ❡❞ ♥❡❣❧✐ ✐♥t❡r✈❛❧❧✐ ♦r❛r✐ ❞❡❧❧❡ r✐❧❡✈❛③✐♦♥✐ s♣❡r✐♠❡♥t❛❧✐✱ ❡ ❧✬❛♥❞❛♠❡♥t♦

❞❡❧❧❡ ❣r❛♥❞❡③③❡ r✐❧❡✈❛t❡ ♠♦str❛ ❝❤❡ ✐❧ ♠♦❞❡❧❧♦ è ✐♥ ❣r❛❞♦ ❞✐ ♣r❡✈❡❞❡r❡ ❝♦♥ ♦tt✐♠❛ ❛♣♣r♦ss✐✲

♠❛③✐♦♥❡ ❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧❧❛ s✉♣❡r✜❝✐❡ ✐♥t❡r♥❛ ❞❡❧ ✈❡tr♦✱ ❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧❧❛ s✉♣❡r✜❝✐❡

❞❡❧ ♣❛✈✐♠❡♥t♦✱ ❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧❧✬❛r✐❛ ❡ ❧❛ t❡♠♣❡r❛t✉r❛ ♠❡❞✐❛ r❛❞✐❛♥t❡ ♣❡r❝❡♣✐t❛ ❞❛ ✉♥❛

♣❡rs♦♥❛ ✐♥ ♣✐❡❞✐ ♥❡❧❧✬❛♠❜✐❡♥t❡ s❡♠✐❝♦♥✜♥❛t♦ ❛❧ ❞✐ s♦tt♦ ❞❡❧❧❛ ❝♦♣❡rt✉r❛✳

■ r✐s✉❧t❛t✐ r✐♣♦rt❛t✐ r✐❣✉❛r❞❛♥♦ ❞✉❡ ❣✐♦r♥❛t❡ s♦❧❡❣❣✐❛t❡✱ ✉♥❛ ❡st✐✈❛ ❡❞ ✉♥❛ ♣r✐♠❛✈❡r✐❧❡✱ ❝❛✲

r❛tt❡r✐③③❛t❡ ❞❛ ❝✐❡❧♦ ❧✐♠♣✐❞♦ ❡ ♣❡r♠❡tt♦♥♦ ❞✐ ♦ss❡r✈❛r❡ ✐❧ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❡❧❧❛ ❝♦♣❡rt✉r❛

✐♥ ✈❡tr♦ ✐♥ ❝♦♥❞✐③✐♦♥✐ ❞✐ ❡❧❡✈❛t❛ ❝♦♠♣♦♥❡♥t❡ ❞✐r❡tt❛ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ❡ ❣❧✐ ❡✛❡tt✐ ❞✐

q✉❡st♦ s✉❧❧❡ ❝♦♥❞✐③✐♦♥✐ ❞✐ ❝♦♠❢♦rt t❡r♠✐❝♦ ♥❡❧❧✬❛♠❜✐❡♥t❡ s❡♠✐❝♦♥✜♥❛t♦✳ ▲✬✐♥❞❛❣✐♥❡✱ ❛♣♣❧✐✲

❝❛♥❞♦ ❧❡ ♠❡❞❡s✐♠❡ ♠♦❞❛❧✐tà ♦♣❡r❛t✐✈❡✱ ♣♦tr❡❜❜❡ ❡ss❡r❡ ❡st❡s❛ ❛ ❣✐♦r♥❛t❡ ❝❛r❛tt❡r✐③③❛t❡ ❞❛

❝✐❡❧♦ ❝♦♣❡rt♦ ♦ ♣✐♦❣❣✐❛✱ ❛♥❝❤❡ ❝♦♥ s♣r❛③③✐ ❞✐ s♦❧❡✱ ❝♦♥s✐❞❡r❛♥❞♦ ♥❡❧❧❛ ♠♦❞❡❧❧❛③✐♦♥❡ ❧✬❡✛❡tt♦

❞❡❧ r❛✛r❡❞❞❛♠❡♥t♦ ❡✈❛♣♦r❛t✐✈♦ s✉❧❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧❧❛ ❝♦♣❡rt✉r❛ ✐♥ ✈❡tr♦✳

✼✼

❙✐♠❜♦❧♦❣✐❛

❙✐♠❜♦❧♦ ●r❛♥❞❡③③❛ ❯♥✐tà ❞✐ ♠✐s✉r❛ ❙■

ρg ❞❡♥s✐tà ✈❡tr♦(

kg/m3)

cg ❝❛❧♦r❡ s♣❡❝✐✜❝♦ ✈❡tr♦ (J/kgK)

Tr t❡♠♣❡r❛t✉r❛ ❝♦♣❡rt✉r❛ (K)

τ t❡♠♣♦ (s)

λg ❝♦♥❞✉tt✐✈✐tà t❡r♠✐❝❛ ✈❡tr♦ (W/mK)

x ❝♦♦r❞✐♥❛t❛ s♣❛③✐❛❧❡ ♥♦r♠❛❧❡ ❛❧❧❛ s✉♣❡r✜❝✐❡ ❞❡❧ ✈❡tr♦ (m)

qg,r r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ❛ss♦r❜✐t❛ ❞❛❧ ✈❡tr♦(

W/m2)

dg s♣❡ss♦r❡ ❞❡❧❧❛ ❧❛str❛ ✐♥ ✈❡tr♦ (m)

ar,b ❝♦❡✣❝✐❡♥t❡ ❞✐ ❛ss♦r❜✐♠❡♥t♦ ❞❡❧ ✈❡tr♦ ❞❡❧❧❛ r❛❞✳ s♦❧❛r❡ ❞✐r❡tt❛

ar,d ❝♦❡✣❝✐❡♥t❡ ❞✐ ❛ss♦r❜✐♠❡♥t♦ ❞❡❧ ✈❡tr♦ ❞❡❧❧❛ r❛❞✳ s♦❧❛r❡ ❞✐✛✉s❛

IT,b r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ❞✐r❡tt❛(

W/m2)

IT,d r❛❞✐❛③✐♦♥❡ s♦❧❛r❡ ❞✐✛✉s❛(

W/m2)

rm ❝♦❡✣❝✐❡♥t❡ ❞✐ r✐✢❡ss✐♦♥❡ ❞❡❧ ❜❛s❛♠❡♥t♦ r❛❞✳ ❞✐r❡tt❛ ❡ ❞✐✛✉s❛

rr,d ❝♦❡✣❝✐❡♥t❡ ❞✐ r✐✢❡ss✐♦♥❡ ❞❡❧ ✈❡tr♦ ❞❡❧❧❛ r❛❞✳ s♦❧❛r❡ ❞✐✛✉s❛

tr,b ❝♦❡✣❝✐❡♥t❡ ❞✐ tr❛s♠✐ss✐♦♥❡ ❞❡❧ ✈❡tr♦ ❞❡❧❧❛ r❛❞✳ s♦❧❛r❡ ❞✐r❡tt❛

tr,d ❝♦❡✣❝✐❡♥t❡ ❞✐ tr❛s♠✐ss✐♦♥❡ ❞❡❧ ✈❡tr♦ ❞❡❧❧❛ r❛❞✳ s♦❧❛r❡ ❞✐✛✉s❛

hc,o ❝♦❡✣❝✐❡♥t❡ ❞✐ ❝♦♥✈❡③✐♦♥❡ ❝♦♣❡rt✉r❛ ✲ ❡st❡r♥♦(

W/m2K)

hc,i ❝♦❡✣❝✐❡♥t❡ ❞✐ ❝♦♥✈❡③✐♦♥❡ ❝♦♣❡rt✉r❛ ✲ ✐♥t❡r♥♦(

W/m2K)

hr,o ❝♦❡✣❝✐❡♥t❡ ❞✐ ✐rr❛❣❣✐❛♠❡♥t♦ ❝♦♣❡rt✉r❛ ✲ ❡st❡r♥♦(

W/m2K)

hr,i ❝♦❡✣❝✐❡♥t❡ ❞✐ ✐rr❛❣❣✐❛♠❡♥t♦ ❝♦♣❡rt✉r❛ ✲ ✐♥t❡r♥♦(

W/m2K)

Tr,o t❡♠♣❡r❛t✉r❛ s✉♣❡r✜❝✐❡ ❡st❡r♥❛ ❝♦♣❡rt✉r❛ (K)

Tr,i t❡♠♣❡r❛t✉r❛ s✉♣❡r✜❝✐❡ ✐♥t❡r♥❛ ❝♦♣❡rt✉r❛ (K)

To t❡♠♣❡r❛t✉r❛ ❛r✐❛ ❛♠❜✐❡♥t❡ ❡st❡r♥♦ (K)

Ti t❡♠♣❡r❛t✉r❛ ❛r✐❛ ❛♠❜✐❡♥t❡ s❡♠✐✲❝♦♥✜♥❛t♦ ✐♥t❡r♥♦ (K)

Tsky t❡♠♣❡r❛t✉r❛ ❞❡❧❧❛ ✈♦❧t❛ ❝❡❧❡st❡ (K)

✼✽

❙✐♠❜♦❧♦ ●r❛♥❞❡③③❛ ❯♥✐tà ❞✐ ♠✐s✉r❛ ❙■

Tm t❡♠♣❡r❛t✉r❛ ❞❡❧❧❛ s✉♣❡r✜❝✐❡ ❞❡❧ ❜❛s❛♠❡♥t♦ (K)

L ❧✉♥❣❤❡③③❛ ❝❛r❛tt❡r✐st✐❝❛ ❞❡❧❧✬❛♠❜✐❡♥t❡ s❡♠✐✲❝♦♥✜♥❛t♦ (m)

Gr ♥✉♠❡r♦ ❞✐ ●r❛s❤♦❢

Re ♥✉♠❡r♦ ❞✐ ❘❡②♥♦❧❞s

σ0 ❝♦st❛♥t❡ ❞✐ ❙t❡❢❛♥✲❇♦❧t③♠❛♥♥ (W/m2K4)

εr ❡♠✐ss✐✈✐tà ✈❡tr♦

εm ❡♠✐ss✐✈✐tà ❜❛s❛♠❡♥t♦

εsky ❡♠✐ss✐✈✐tà ✈♦❧t❛ ❝❡❧❡st❡

ρa ❞❡♥s✐tà ❛r✐❛(

kg/m3)

ca ❝❛❧♦r❡ s♣❡❝✐✜❝♦ ❛r✐❛ (J/kgK)

Hav ❛❧t❡③③❛ ♠❡❞✐❛ ❞❡❧❧❛ ❝♦♣❡rt✉r❛ (m)

Lr ❧✉♥❣❤❡③③❛ ❞❡❧❧❛ ❝♦♣❡rt✉r❛ (m)

hc,m ❝♦❡✣❝✐❡♥t❡ ❞✐ ❝♦♥✈❡③✐♦♥❡ ❜❛s❛♠❡♥t♦(

W/m2K)

Va ✈❡❧♦❝✐tà ❞❡❧❧✬❛r✐❛ ♥❡❧❧✬❛♠❜✐❡♥t❡ s❡♠✐✲❝♦♥✜♥❛t♦ (m/s)

ρm ❞❡♥s✐tà s✐♥❣♦❧♦ str❛t♦ ❞✐ ❜❛s❛♠❡♥t♦(

kg/m3)

cm ❝❛❧♦r❡ s♣❡❝✐✜❝♦ s✐♥❣♦❧♦ str❛t♦ ❞✐ ❜❛s❛♠❡♥t♦ (J/kgK)

λm ❝♦♥❞✉tt✐✈✐tà t❡r♠✐❝❛ s✐♥❣♦❧♦ str❛t♦ ❞✐ ❜❛s❛♠❡♥t♦ (W/mK)

dm s♣❡ss♦r❡ s✐♥❣♦❧♦ str❛t♦ ❞✐ ❜❛s❛♠❡♥t♦ (m)

am ❝♦❡✣❝✐❡♥t❡ ❞✐ ❛ss♦r❜✐♠❡♥t♦ ❞❡❧ ❜❛s❛♠❡♥t♦ ❞❡❧❧❛ r❛❞✐❛③✐♦♥❡ s♦❧❛r❡

Gsc ❝♦st❛♥t❡ s♦❧❛r❡(

W/m2)

✼✾

❘✐❢❡r✐♠❡♥t✐ ❜✐❜❧✐♦❣r❛✜❝✐

❬✶❪ ❆❙❍❘❆❊ ❍❛♥❞❜♦♦❦✲❋✉♥❞❛♠❡♥t❛❧s✱ ❆♠❡r✐❝❛♥ ❙♦❝✐❡t② ♦❢ ❍❡❛t✐♥❣✱ ❘❡❢r✐❣❡r❛t✐♥❣ ❛♥❞❆✐r✲❈♦♥❞✐t✐♦♥✐♥❣ ❊♥❣✐♥❡❡rs✱ ■♥❝✳✱ ❆t❧❛♥t❛✱ ✷✵✵✶

❬✷❪ ❲✳ ❇♦❧t♦♥✱ ▼❡❝❤❛tr♦♥✐❝s ✲ ❊❧❡❝tr♦♥✐❝ ❝♦♥tr♦❧ s②st❡♠s ✐♥ ♠❡❝❤❛♥✐❝❛❧ ❡♥❣✐♥❡❡r✐♥❣✱❆❞❞✐s♦♥ ❲❡s❧❡② ▲♦♥❣♠❛♥✱ ◆❡✇ ❨♦r❦ ✶✾✾✾

❬✸❪ ●✳❈❛♥♥✐str❛r♦✱ ●✳❋r❛♥③✐tt❛✱ ❈✳ ●✐❛❝♦♥✐❛✱ ●✳ ❘✐③③♦✱ ❆❧❣♦r✐t❤♠s ❢♦r t❤❡ ❝❛❧❝✉❧❛t✐♦♥♦❢ t❤❡ ✈✐❡✇ ❢❛❝t♦rs ❜❡t✇❡❡♥ ❤✉♠❛♥ ❜♦❞② ❛♥❞ r❡❝t❛♥❣✉❧❛r s✉r❢❛❝❡s ✐♥ ♣❛r❛❧❧❡❧❡♣✐♣❡❞❡♥✈✐r♦♥♠❡♥ts✱ ❊♥❡r❣② ❛♥❞ ❇✉✐❧❞✐♥❣s✱ ✈♦❧ ✶✾✱ ♣♣✳ ✺✶✕✻✵✱ ✶✾✾✷

❬✹❪ ❘✳❉✳ ❈❧❡❛r✱ ▲✳ ●❛rt❧❛♥❞✱ ❋✳❈✳ ❲✐♥❦❡❧♠❛♥♥✱ ❆♥ ❡♠♣✐r✐❝❛❧ ❝♦rr❡❧❛t✐♦♥ ❢♦r t❤❡ ♦✉ts✐❞❡❝♦♥✈❡❝t✐✈❡ ❛✐r✲✜❧♠ ❝♦❡✣❝✐❡♥t ❢♦r ❤♦r✐③♦♥t❛❧ r♦♦❢s✱ ❊♥❡r❣② ❛♥❞ ❇✉✐❧❞✐♥❣s✱ ✈♦❧ ✸✺✱ ♣♣✳✼✾✼✕✽✶✶✱ ✷✵✵✸

❬✺❪ ▼✳ ❉❛❧❧✬❆❝q✉❛ ✭❛ ❝✉r❛ ❞✐✮✱ ❊♥❝✐❝❧♦♣❡❞✐❛ ❞✐ P❛r♠❛✳ ❉❛❧❧❡ ♦r✐❣✐♥✐ ❛✐ ❣✐♦r♥✐ ♥♦str✐✱❋r❛♥❝♦ ▼❛r✐❛ ❘✐❝❝✐✱ P❛r♠❛ ✶✾✾✽

❬✻❪ ❏♦❤♥ ❆✳ ❉✉✣❡✱ ❲✐❧❧✐❛♠ ❆✳ ❇❡❝❦♠❛♥✱ ❙♦❧❛r ❊♥❣✐♥❡❡r✐♥❣ ❚❤❡r♠❛❧ Pr♦❝❡ss♦r✱ ❏♦❤♥❲✐❧❡② ✫ ❙♦♥s✱ ■♥❝✳✱ ✶✾✽✵

❬✼❪ P✳❖✳ ❋❛♥❣❡r✱ ❚❤❡r♠❛❧ ❈♦♠❢♦rt ✲ ❆♥❛❧②s✐s ❛♥❞ ❆♣♣❧✐❝❛t✐♦♥s ✐♥ ❊♥✈✐r♦♥♠❡♥t❛❧❊♥❣✐♥❡❡r✐♥❣✱ ❉❛♥✐s❤ ❚❡❝❤♥✐❝❛❧ Pr❡ss✱ ❈♦♣❡♥❤❛❣❡♥✱ ✶✾✼✵

❬✽❪ ❆❞❡❧ ❆✳ ❍❡❣❛③②✱ ❊✛❡❝t ♦❢ ❞✉st ❛❝❝✉♠✉❧❛t✐♦♥ ♦♥ s♦❧❛r tr❛♥s♠✐tt❛♥❝❡ t❤r♦✉❣❤ ❣❧❛ss❝♦✈❡rs ♦❢ ♣❧❛t❡✲t②♣❡ ❝♦❧❧❡❝t♦rs✱ ❘❡♥❡✇❛❜❧❡ ❊♥❡r❣②✱ ✈♦❧✳ ✷✷✱ ♣♣✳ ✺✷✺✕✺✹✵✱ ✷✵✵✶

❬✾❪ P✳ ❍ö♣♣❡✱ ❉✐✛❡r❡♥t ❛s♣❡❝ts ♦❢ ❛ss❡ss✐♥❣ ✐♥❞♦♦r ❛♥❞ ♦✉t❞♦♦r t❤❡r♠❛❧ ❝♦♠❢♦rt✱ ❊♥❡r❣②❛♥❞ ❇✉✐❧❞✐♥❣s✱ ✈♦❧✳ ✸✹✱ ♣♣✳ ✻✻✶✕✻✻✺✱ ✷✵✵✷

❬✶✵❪ P✳ ❍ö♣♣❡✱ ❚❤❡ ♣❤②s✐♦❧♦❣✐❝❛❧ ❡q✉✐✈❛❧❡♥t t❡♠♣❡r❛t✉r❡✿ ❛ ✉♥✐✈❡rs❛❧ ✐♥❞❡① ❢♦r t❤❡ ❜✐♦✲♠❡t❡♦r♦❧♦❣✐❝❛❧ ❛ss❡ss♠❡♥t ♦❢ t❤❡ t❤❡r♠❛❧ ❡♥✈✐r♦♥♠❡♥t✱ ■♥t❡r♥❛t✐♦♥❛❧ ❏♦✉r♥❛❧ ♦❢❇✐♦♠❡t❡♦r♦❧♦❣②✱ ✈♦❧✳ ✹✸✱ ♣♣✳ ✼✶✕✼✺✱ ✶✾✾✾

❬✶✶❪ ❋✳P✳ ■♥❝r♦♣❡r❛✱ ❉✳P✳ ❉❡ ❲✐tt✱ ❋✉♥❞❛♠❡♥t❛❧s ♦❢ ❍❡❛t ❛♥❞ ▼❛ss ❚r❛♥s❢❡r✱ ❏✳❲✐❧❡② ✫❙♦♥s✱ ◆❡✇ ❨♦r❦✱ ✶✾✾✵

❬✶✷❪ ▼✳ ▲❛ ●❡♥♥✉s❛✱ ❆✳ ◆✉❝❛r❛✱ ●✳ ❘✐③③♦✱ ●✳ ❙❝❛❝❝✐❛♥♦❝❡✱ ❚❤❡ ❝❛❧❝✉❧❛t✐♦♥ ♦❢ t❤❡ ♠❡❛♥ r❛✲❞✐❛♥t t❡♠♣❡r❛t✉r❡ ♦❢ ❛ s✉❜❥❡❝t ❡①♣♦s❡❞ t♦ t❤❡ s♦❧❛r r❛❞✐❛t✐♦♥ ✲ ❛ ❣❡♥❡r❛❧✐s❡❞ ❛❧❣♦r✐t❤♠✱❇✉✐❧❞✐♥❣ ❛♥❞ ❊♥✈✐r♦♥♠❡♥t✱ ✈♦❧✳ ✹✵✱ ♣♣✳ ✸✻✼✲✸✼✺✱ ✷✵✵✺

❬✶✸❪ ▼❊❚❊❖◆❖❘▼ ●❧♦❜❛❧ ▼❡t❡♦r♦❧♦❣✐❝❛❧ ❉❛t❛❜❛s❡ ❢♦r ❙♦❧❛r ❊♥❡r❣② ❛♥❞ ❆♣♣❧✐❡❞❈❧✐♠❛t♦❧♦❣②✱ ❱❡rs✐♦♥ ✺✱ ✭❤tt♣✿✴✴✇✇✇✳♠❡t❡♦t❡st✳❝♦♠✮

❬✶✹❪ ●✳P❛❣❧✐❛r✐♥✐✱ ❆♥❛❧✐s✐ ❞❡❧❧❡ ❝♦♥❞✐③✐♦♥✐ t❡r♠✐❝❤❡ ❛ss♦❝✐❛t❡ ❛❧ ♥✉♦✈♦ s✐st❡♠❛ ❞✐ ❝♦♣❡rt✉r❛♥❡❧❧✬❛r❡❛ st♦r✐❝❛ ✉r❜❛♥❛ ❞✐ ♣✐❛③③❛ ●❤✐❛✐❛ ✐♥ P❛r♠❛ ✲ ❘❡❧❛③✐♦♥❡ ❝♦♥❝❧✉s✐✈❛

❬✶✺❪ ●✳ P❛❣❧✐❛r✐♥✐✱ ❙✳ ❘❛✐♥✐❡r✐✱ ❉②♥❛♠✐❝ t❤❡r♠❛❧ s✐♠✉❧❛t✐♦♥ ♦❢ ❛ ❣❧❛ss✲❝♦✈❡r❡❞ s❡♠✐✲♦✉t❞♦♦rs♣❛❝❡ ✇✐t❤ r♦♦❢ ❡✈❛♣♦r❛t✐✈❡ ❝♦♦❧✐♥❣✱ ❊♥❡r❣② ❛♥❞ ❇✉✐❧❞✐♥❣s✱ ✈♦❧✳ ✹✸✱ ♣♣✳ ✺✾✷✲✺✾✽✱ ✷✵✵✶

✽✵

❬✶✻❪ ●✳ P❛❣❧✐❛r✐♥✐✱ ❙✳ ❘❛✐♥✐❡r✐✱ ❚❤❡r♠❛❧ ❡♥✈✐r♦♥♠❡♥t ❝❤❛r❛❝t❡r✐s❛t✐♦♥ ♦❢ ❛ ❣❧❛ss✲❝♦✈❡r❡❞s❡♠✐✲♦✉t❞♦♦r s♣❛❝❡ s✉❜❥❡❝t❡❞ t♦ ♥❛t✉r❛❧ ❝❧✐♠❛t❡ ♠✐t✐❣❛t✐♦♥✱ ❊♥❡r❣② ❛♥❞ ❇✉✐❧❞✐♥❣s✱✈♦❧✳ ✹✸✱ ♣♣✳ ✶✻✵✾✲✶✻✶✼✱ ✷✵✶✶

❬✶✼❪ ●✳▼✳ ❘❛♣♣✱ ❆✳P✳ ●❛❣❣❡✱ ❈♦♥✜❣✉r❛t✐♦♥ ❢❛❝t♦rs ❛♥❞ ❝♦♠❢♦rt ❞❡s✐❣♥ ✐♥ r❛❞✐❛♥t ❜❡❛♠❤❡❛t✐♥❣ ♦❢ ♠❛♥ ❜② ❤✐❣❤ t❡♠♣❡r❛t✉r❡ ✐♥❢r❛r❡❞ s♦✉r❝❡s✱ ❆❙❍❘❆❊ ❚r❛♥s✳✱ ✈♦❧✳✼✸ ✭P❛rt■■✮✱ ✶✾✻✼

❬✶✽❪ ●✳▼✳ ❘❛♣♣✱ ❆✳P✳ ●❛❣❣❡✱ ❍✐❣❤ ✐♥t❡♥s✐t② r❛❞✐❛♥t ❤❡❛t✐♥❣✱ ❆❙❍❘❆❊ ●✉✐❞❡ ❛♥❞ ❉❛t❛❇♦♦❦✿ ❙②st❡♠s✱ ❈❤✳✶✼✱ ✶✾✼✵

❬✶✾❪ ●✳ ❘✐③③♦✱ ●✳ ❋r❛♥③✐tt❛✱ ●✳ ❈❛♥♥✐str❛r♦✱ ❆❧❣♦r✐t❤♠s ❢♦r t❤❡ ❝❛❧❝✉❧❛t✐♦♥ ♦❢ t❤❡ ♠❡❛♥♣r♦❥❡❝t❡❞ ❛r❡❛ ❢❛❝t♦rs ♦❢ s❡❛t❡❞ ❛♥❞ st❛♥❞✐♥❣ ♣❡rs♦♥s✱ ❊♥❡r❣② ❛♥❞ ❇✉✐❧❞✐♥❣s✱ ✈♦❧✳ ✶✼✱♣♣✳ ✷✷✶✕✷✸✵✱ ✶✾✾✶

❬✷✵❪ ❋✳ ❘✉t③✱ ❆✳ ▼❛t③❛r❛❦✐s✱ ❍✳ ▼❛②❡r✱ ❘❛②▼❛♥ ❱❡rs✐♦♥ ✶✳✷ ✲ ▼♦❞❡❧❧✐♥❣ ♦❢ ♠❡❛♥ r❛❞✐❛♥tt❡♠♣❡r❛t✉r❡ ✐♥ ✉r❜❛♥ str✉❝t✉r❡s ✲ ❝❛❧❝✉❧❛t✐♦♥ ♦❢ t❤❡r♠❛❧ ✐♥❞✐❝❡s✱ ❋r❡✐❜✉r❣✱ ✷✵✵✵

❬✷✶❪ ❏✳ ❙♣❛❣♥♦❧♦✱ ❘✳ ❞❡ ❉❡❛r✱ ❆ ✜❡❧❞ st✉❞② ♦❢ t❤❡r♠❛❧ ❝♦♠❢♦rt ✐♥ ♦✉t❞♦♦r ❛♥❞ s❡♠✐✲♦✉t❞♦♦r❡♥✈✐r♦♥♠❡♥ts ✐♥ s✉❜tr♦♣✐❝❛❧ ❙②❞♥❡②✱ ❆✉str❛❧✐❛✱ ❇✉✐❧❞✐♥❣ ❛♥❞ ❊♥✈✐r♦♥♠❡♥t✱ ✈♦❧✳ ✸✽✱ ♣♣✳✼✷✶✕✼✸✽✱ ✷✵✵✸

❬✷✷❪ ▼✳❙t❡✐♥♠❛♥✱ ▲✳◆✳ ❑❛❧✐s♣❡r✐s✱ ▲✳❍✳ ❙✉♠♠❡rs✱ ❆♥❣❧❡ ❢❛❝t♦r ❞❡t❡r♠✐♥❛t✐♦♥ ❢r♦♠ ❛♣❡rs♦♥ t♦ ✐♥❝❧✐♥❡❞ s✉r❢❛❝❡s✱ ❆❙❍❘❆❊ ❚r❛♥s✳✱ ✈♦❧✳ ✾✹ ✭P❛rt ■✮✱ ♣♣✳ ✶✽✵✾✲✶✽✷✸✱ ✶✾✽✽

❬✷✸❪ ❊◆ ■❙❖ ✼✼✷✻✱ ❊r❣♦♥♦♠✐❝s ♦❢ t❤❡ t❤❡r♠❛❧ ❡♥✈✐r♦♥♠❡♥t ✐♥str✉♠❡♥ts ❢♦r ♠❡❛s✉r✐♥❣♣❤②s✐❝❛❧ q✉❛♥t✐t✐❡s✱ ✷✵✵✶

❬✷✹❪ ❯◆■ ✶✵✸✺✶✱ ▼❛t❡r✐❛❧✐ ❞❛ ❝♦str✉③✐♦♥❡ ✲ ❈♦♥❞✉tt✐✈✐tà t❡r♠✐❝❛ ❡ ♣❡r♠❡❛❜✐❧✐tà ❛❧ ✈❛♣♦r❡✱✶✾✾✹

❬✷✺❪ ❯◆■ ❊◆ ✹✶✵✱ ❱❡tr♦ ♣❡r ❡❞✐❧✐③✐❛ ✲ ❉❡t❡r♠✐♥❛③✐♦♥❡ ❞❡❧❧❡ ❝❛r❛tt❡r✐st✐❝❤❡ ❧✉♠✐♥♦s❡ ❡ s♦❧❛r✐❞❡❧❧❡ ✈❡tr❛t❡✱ ✷✵✵✶

✽✶

i

%%%% Con copertura, posizione persona in piedi al centro dello spazio %%%% clear clc close all load ingressi_1h.txt; load ingressi_10s.txt; load ingressi_15s.txt; %% Dati iniziali % Dati acquisiti lunedì 30.07.2012 %%% T_min=5051; ore=3; T_max=T_min+ore; T_air_internal=29.5; T_glass=45.562; T_basement=37.291; %% Definizione della geometria %%% sps=0.01952; % spessore copertura (m) dato fornito da Serex alfa=5; % pendenza copertura sps_m=0.3; % spessore pavimento (m) H1=4.5; % altezza lato basso (m) elle=8*H1; % lunghezza pavimento (m) elle_C=elle/cos(alfa/180*pi); % lunghezza copertura (m) H2=H1+elle*tan(alfa*pi/180); % altezza lato alto (m) H_m=(H1+H2)/2; %% Passo d'integrazione % vetro dtau=2; N_dx=2; N_dx1=N_dx+1; dx=sps/N_dx; % pavimento dtau_m=dtau; sps_m_p=0.05; % spessore strato porfido N_dx_m_p=5; dx_m_p=sps_m_p/N_dx_m_p; sps_m_m=0.05; % spessore strato malta N_dx_m_m=5; dx_m_m=sps_m_m/N_dx_m_m; sps_m_c=0.1; % spessore strato calcestruzzo N_dx_m_c=10; dx_m_c=sps_m_c/N_dx_m_c; sps_m_a=0.1; % spessore strato alleggerito N_dx_m_a=10; dx_m_a=sps_m_a/N_dx_m_a; N_dx_m=N_dx_m_p+N_dx_m_m+N_dx_m_c+N_dx_m_a; N_dx1_m=N_dx_m+1; %% Costanti %%% g=9.81; T0=273.15; sigma=5.67E-8; %% Proprietà vetro angolo_incidenza=xlsread('ingressi.xlsx','vetro','b9:b18')'; trasmissione=xlsread('ingressi.xlsx','vetro','c9:c18')';

ii

assorbimento=xlsread('ingressi.xlsx','vetro','d9:d18')'; tr_emi=xlsread('ingressi.xlsx','vetro','c3'); ass_emi=xlsread('ingressi.xlsx','vetro','c4'); V_dir=[angolo_incidenza;trasmissione;assorbimento]'; V_dif=[tr_emi;ass_emi]'; t_dif=V_dif(1); a_dif=V_dif(2); r_dif=1-a_dif-t_dif; cond_V=1.; C_V=2500*840; % J/m3°C (capacità volumica vetro) a_1=0.95; % coeff. assorbimento infrarosso a_1=0.95 %% Proprietà pavimento a_b=0.75; % coeff. di assorbimento per la radiazione solare r_b=1-a_b; %Porfido 5 cm cond_m_p=2.90; % conducibilità Cmi_p=2200*840*sps_m_p; % J/°C m2 (capacità termica interna per m2) Cmi_V_p=2200*840; % J/m3 °C (capacità volumica) %Malta 5 cm cond_m_m=1.4; % conducibilità Cmi_m=2000*840*sps_m_m; % J/°C m2 (capacità termica interna per m2) Cmi_V_m=2000*840; % J/m3 °C (capacità volumica) %Calcestruzzo 10 cm cond_m_c=1.48; % conducibilità Cmi_c=2200*840*sps_m_c; % J/°C m2 (capacità termica interna per m2) Cmi_V_c=2200*840; % J/m3 °C (capacità volumica) %Alleggerito 10 cm cond_m_a=0.42; % conducibilità Cmi_a=700*840*sps_m_a; % J/°C m2 (capacità termica interna per m2) Cmi_V_a=700*840; % J/m3 °C (capacità volumica) %% Fattori di forma delle superfici rispetto alla persona in piedi al centro dello spazio h=1.1; % quota punto di rilevamento (in piedi) Fmax1=0.120; Fmax2=0.116; A1=1.24186; A2=1.59512; B1=0.16730; B2=0.12788; C1=0.61648; C2=1.22643; D1=0.08165; D2=0.04621; E1=0.05128; E2=0.04434; a=elle/2; b=10^10; c=h; tau=A2+B2*(a/c); gamma=C2+D2*(b/c)+E2*(a/c); F_p=4*Fmax2*(1-exp(-(a/c)/tau))*(1-exp(-(b/c)/gamma)); % fattore di vista rispetto al pavimento a=h; c=elle/2; tau=A1+B1*(a/c); gamma=C1+D1*(b/c)+E1*(a/c); F1=2*Fmax1*(1-exp(-(a/c)/tau))*(1-exp(-(b/c)/gamma)); % fattore di vista rispetto ai due rettangoli verticali inferiori (rispetto al centro della persona) F2=F1; a=H1-h; tau=A1+B1*(a/c);

iii

gamma=C1+D1*(b/c)+E1*(a/c); F1=F1+2*Fmax1*(1-exp(-(a/c)/tau))*(1-exp(-(b/c)/gamma)); % fattore di vista rispetto ai due rettangoli verticali inferiori e ai due superiori (rispetto al centro della persona) per il lato basso H1 a=H2-h; tau=A1+B1*(a/c); gamma=C1+D1*(b/c)+E1*(a/c); F2=F2+2*Fmax1*(1-exp(-(a/c)/tau))*(1-exp(-(b/c)/gamma)); % fattore di vista rispetto ai due rettangoli verticali inferiori e ai due superiori (rispetto al centro della persona) per il lato alto H2 F=F1+F2; % fattore di vista rispetto ai due piani verticali F_c=1-F_p-F; % fattore di vista rispetto al soffitto %% Projected area factor PAF=[0,15,30,45,60,75,90;0.304,0.304,0.272,0.222,0.175,0.122,0.082]'; % in piedi %% Proprietà aria%%% ni=[250,280,300,320,340,360;1.14*10^-5,1.43*10^-5,1.61*10^-5,1.8*10^-5,1.99*10^-5,2.2*10^-5]'; cond=[250,280,300,320,340,360;0.0223,0.0246,0.0262,0.0277,0.0292,0.0307]'; ro=[250,280,300,320,340,360;1.39,1.26,1.18,1.11,1.04,0.98]'; cp=[250,280,300,320,340,360;1005,1005,1005,1006,1008,1010]'; Pr=0.71; %% Calore latente%%% r=[240,260,280,300,320,340,360,380;2485,2485,2485,2437,2390,2341,2291,2238]'; % kJ/kg %% Proprietà radiative corpo umano%%% ak=0.7; % coeff. assorbimento superficie irraggiata dal sole ep=0.97; % coeff. emissione corpo umano %% Valori iniziali%%% Q_e=0.; Q_i=0.; Q_mi=0.; i=0; %% Inizio calcolo for i_ora=T_min:T_max-1; i_ora; for i_s=1:dtau:3600; i=i+1; ii=i_ora+i_s/3600.; Te(i)=interp1(ingressi_1h(:,1),ingressi_1h(:,2),ii); %°C FI(i)=interp1(ingressi_1h(:,1),ingressi_1h(:,4),ii); %UR V(i)=interp1(ingressi_1h(:,1),ingressi_1h(:,3),ii); % esterno m/s T_sky(i)=interp1(ingressi_1h(:,1),ingressi_1h(:,5),ii); %°C W(i)=interp1(ingressi_15s(:,1),ingressi_15s(:,2),ii); % interno m/s R_dir(i)=interp1(ingressi_10s(:,1),ingressi_10s(:,2),ii); %W/m2 R_dif(i)=interp1(ingressi_10s(:,1),ingressi_10s(:,3),ii); %W/m2 RD(i)=interp1(ingressi_10s(:,1),ingressi_10s(:,4),ii); %W/m2 angolo(i)=interp1(ingressi_10s(:,1),ingressi_10s(:,5),ii); %° %%%Condizione iniziale ore 11%%% if (i==1) Ti(1)=T_air_internal; T(1,1:N_dx1)=T_glass; T_mi(1,1:N_dx1_m)=T_basement; end if (angolo(i)>90); angolo(i)=90; end

iv

t_dir=interp1(V_dir(:,1),V_dir(:,2),angolo(i)); % coeff. trasmissione a_dir=interp1(V_dir(:,1),V_dir(:,3),angolo(i)); % coeff. assorbimento r_dir=1-t_dir-a_dir; %%%Proprietà dell'aria INTERNO%%% ro_air=interp1(ro(:,1),ro(:,2),Ti(i)+T0); cp_air=interp1(cp(:,1),cp(:,2),Ti(i)+T0); RCaria=ro_air*cp_air; Ca=RCaria*H_m; % J/°C m2 (capacità termica media aria per m2 di pavimento) Q_vt(i)=W(i)*H_m; %%%Proprietà dell'aria ESTERNO%%% T_film=(T(i,1)+Te(i))/2+T0; ni_air=interp1(ni(:,1),ni(:,2),T_film); cond_air=interp1(cond(:,1),cond(:,2),T_film); beta=1/T_film; %espressione del coefficiente di convezione mista da R.D. Clear et al.% Rf=1; % fattore scabrezza superficie Re=V(i)*elle_C/ni_air; X_cr=elle_C/Re*5*10^5; delta_Tce(i)=T(i,1)-Te(i); Gr=g*beta*(elle_C/2)^3*abs(delta_Tce(i))/ni_air^2; Ra=Gr*Pr; eta0=log(1+Gr/Re^2); eta=eta0/(1+eta0); if (delta_Tce(i)>=0.); hcf_e(i)=cond_air/elle_C*Rf*0.037*Re^(4/5)*Pr^(1/3); hcn_e(i)=cond_air/(elle_C/2)*0.15*Ra^(1/3); elseif (delta_Tce(i)<0.); if (elle_C>X_cr) hcf_e(i)=cond_air/elle_C*Rf*(0.037*Re^(4/5)-871)*Pr^(1/3); else hcf_e(i)=cond_air/elle_C*Rf*0.664*Re^(1/2)*Pr^(1/3); end hcn_e(i)=cond_air/(elle_C/2)*0.27*Ra^(1/4); end hc_e(i)=hcf_e(i)+eta*hcn_e(i); % coeff. irraggiamento esterno copertura hr_e(i)=a_1*sigma*((T_sky(i)+T0)^2+(T(i,1)+T0)^2)*((T_sky(i)+T0)+(T(i,1)+T0)); %%%Proprietà dell'aria INTERNO- copertura%%% T_film=(T(i,N_dx1)+Ti(i))/2+T0; ni_air=interp1(ni(:,1),ni(:,2),T_film); cond_air=interp1(cond(:,1),cond(:,2),T_film); beta=1/T_film; %convezione interna + irraggiamento interno (copertura) delta_Tc(i)=Ti(i)-T(i,N_dx1); Re=W(i)*elle_C/ni_air; Gr=g*beta*(elle_C/2)^3*abs(delta_Tc(i))/ni_air^2; Ra=Gr*Pr; X_cr=elle_C/Re*5*10^5; eta0=log(1+Gr/Re^2); eta=eta0/(1+eta0); if (delta_Tc(i)>=0.) hcf_i(i)=cond_air/elle_C*Rf*0.037*Re^(4/5)*Pr^(1/3); hcn_i(i)=cond_air/(elle_C/2)*0.15*Ra^(1/3); elseif (delta_Tc(i)<0.) if (elle_C>X_cr) hcf_i(i)=cond_air/elle_C*Rf*(0.037*Re^(4/5)-871)*Pr^(1/3); else hcf_i(i)=cond_air/elle_C*Rf*0.664*Re^(1/2)*Pr^(1/3); end hcn_i(i)=cond_air/(elle_C/2)*0.27*Ra^(1/4); end hc_i(i)=hcf_i(i)+eta*hcn_i(i); hr_i(i)=a_1*sigma*((T_mi(i,1)+T0)^2+(T(i,N_dx1)+T0)^2)*((T_mi(i,1)+T0)+(T(i,N_dx1)+T0)); % coeff. irraggiamento interno copertura

v

%%%Proprietà dell'aria INTERNO- pavimento%%% T_film=(T_mi(i,1)+Ti(i))/2+T0; ni_air=interp1(ni(:,1),ni(:,2),T_film); beta=1/T_film; %convezione interna (capacità termica) delta_Tm(i)=T_mi(i,1)-Ti(i); Re=W(i)*elle/ni_air; Gr=g*beta*elle^3*abs(delta_Tm(i))/ni_air^2; Ra=Gr*Pr; X_cr=elle/Re*5*10^5; eta0=log(1+Gr/Re^2); eta=eta0/(1+eta0); if (delta_Tm(i)>=0.) hcf_m(i)=cond_air/elle*Rf*0.037*Re^(4/5)*Pr^(1/3); hcn_m(i)=cond_air/(elle/2)*0.15*Ra^(1/3); elseif (delta_Tm(i)<0.) if (elle>X_cr) hcf_m(i)=cond_air/elle*Rf*(0.037*Re^(4/5)-871)*Pr^(1/3); else hcf_m(i)=cond_air/elle*Rf*0.664*Re^(1/2)*Pr^(1/3); end hcn_m(i)=cond_air/(elle/2)*0.27*Ra^(1/4); end hc_m(i)=hcf_m(i)+eta*hcn_m(i); % Risoluzione dell'equazione di Fourier nel vetro T_lim=(T_max-1-T_min+1)*3600/dtau; if (i~=T_lim); Qg_r(i)=(a_dir*R_dir(i)+a_dif*R_dif(i)+a_dif*r_b/(1-r_dif*r_b)*(t_dir*R_dir(i)+t_dif*R_dif(i))); % radiazione solare assorbita dalla copertura (W/m2) T(i+1,1)=T(i,1)+dtau/(C_V*dx/2)*(cond_V/dx*(T(i,2)-T(i,1))+hc_e(i)*(Te(i)-T(i,1))+hr_e(i)*(T_sky(i)-T(i,1))+Qg_r(i)*(0.5/N_dx)); for j=2:N_dx; T(i+1,j)=T(i,j)+dtau/(C_V*dx)*(cond_V/dx*(T(i,j+1)+T(i,j-1)-2*T(i,j))+Qg_r(i)*(1/N_dx)); end T(i+1,N_dx1)=T(i,N_dx1)+dtau/(C_V*dx/2)*(cond_V/dx*(T(i,N_dx)-T(i,N_dx1))+hc_i(i)*(Ti(i)-T(i,N_dx1))+hr_i(i)*(T_mi(i,1)-T(i,N_dx1))+Qg_r(i)*(0.5/N_dx)); % Bilancio energetico dell'aria interna Ti(i+1)=Ti(i)+dtau/Ca*(hc_i(i)*elle_C/elle*(T(i,N_dx1)-Ti(i))+hc_m(i)*(T_mi(i,1)-Ti(i))+Q_vt(i)*RCaria/elle*(Te(i)-Ti(i))); % Risoluzione dell'equazione di Fourier nel pavimento T_lim=(T_max-1-T_min+1)*3600/dtau_m; if (i~=T_lim); Qg_m(i)=a_b/(1-r_dif*r_b)*(t_dir*R_dir(i)+t_dif*R_dif(i)); % radiazione solare assorbita dal pavimento (W/m2) %Porfido T_mi(i+1,1)=T_mi(i,1)+dtau_m/(Cmi_V_p*dx_m_p/2)*(cond_m_p/dx_m_p*(T_mi(i,2)-T_mi(i,1))+hc_m(i)*(Ti(i)-T_mi(i,1))+hr_i(i)*(T(i,N_dx1)-T_mi(i,1))+Qg_m(i)); for j=2:N_dx_m_p; T_mi(i+1,j)=T_mi(i,j)+dtau_m/(Cmi_V_p*dx_m_p)*(cond_m_p/dx_m_p*(T_mi(i,j+1)+T_mi(i,j-1)-2*T_mi(i,j))); end %Malta for j=N_dx_m_p+1:N_dx_m_c; T_mi(i+1,j)=T_mi(i,j)+dtau_m/(Cmi_V_m*dx_m_m)*(cond_m_m/dx_m_m*(T_mi(i,j+1)+T_mi(i,j-1)-2*T_mi(i,j))); end %Calcestruzzo for j=N_dx_m_c+1:N_dx_m_c+N_dx_m_a;

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T_mi(i+1,j)=T_mi(i,j)+dtau_m/(Cmi_V_c*dx_m_c)*(cond_m_c/dx_m_c*(T_mi(i,j+1)+T_mi(i,j-1)-2*T_mi(i,j))); end %Alleggerito for j=N_dx_m_c+N_dx_m_a+1:N_dx_m; T_mi(i+1,j)=T_mi(i,j)+dtau_m/(Cmi_V_a*dx_m_a)*(cond_m_a/dx_m_a*(T_mi(i,j+1)+T_mi(i,j-1)-2*T_mi(i,j))); end T_mi(i+1,N_dx1_m)=T_mi(i+1,N_dx_m); % Calcolo dell'energia scambiata nel periodo % Qec(i)=hc_e(i)*(Te(i)-T(i,1)); Qer(i)=hr_e(i)*(T_sky(i)-T(i,1)); Qe(i)=Qec(i)+Qer(i); Qe_rap(i)=Qer(i)/Qec(i); Q_e=Q_e+(Qe(i)+Qg_r(i))*dtau; Qic(i)=hc_i(i)*(T(i,N_dx1)-Ti(i)); Qir(i)=hr_i(i)*(T(i,N_dx1)-T_mi(i,1)); Qi(i)=Qic(i)+Qir(i); Q_i=Q_i+Qi(i)*dtau; Q_mi=Q_mi+(hc_m(i)*(Ti(i)-T_mi(i,1))+hr_i(i)*(T(i,N_dx1)-T_mi(i,1))+Qg_m(i))*dtau; Qg_rr(i)=(r_dir*R_dir(i)+r_dif*R_dif(i)+r_b*(1-a_dif)*(1-r_dif)/(1-r_b*r_dif)*(t_dir*R_dir(i)+t_dif*R_dif(i))); % parte della radiazione riflessa dal basamento che va alla volta celeste R_totale(i)=(R_dir(i)+R_dif(i)); DR(i)=R_totale(i)-(Qg_r(i)+Qg_m(i)+Qg_rr(i)); %%%Calcolo della temperatura media radiante%%% fp(i)=interp1(PAF(:,1),PAF(:,2),90-angolo(i)); Tmr(i)=(F_c*(T(i,N_dx1)+T0)^4+F_p*(T_mi(i,1)+T0)^4+F*(T_sky(i)+T0)^4+((F+F_c*t_dif)*R_dif(i)+F_p*Qg_m(i)*r_b/a_b+fp(i)*t_dir*RD(i))*ak/ep/sigma)^0.25; % Andreas Matzarakis & Frank Rutz & Helmut Mayer Tmr(i)=Tmr(i)-T0; end end end end %% Calcolo temperature medie (5 min) % Glass temperature T_mean_1=mean(T(1:149,N_dx1)); T_mean_2=mean(T(150:299,N_dx1)); T_mean_3=mean(T(300:449,N_dx1)); T_mean_4=mean(T(450:599,N_dx1)); T_mean_5=mean(T(600:749,N_dx1)); T_mean_6=mean(T(750:899,N_dx1)); T_mean_7=mean(T(900:1049,N_dx1)); T_mean_8=mean(T(1050:1199,N_dx1)); T_mean_9=mean(T(1200:1349,N_dx1)); T_mean_10=mean(T(1350:1499,N_dx1)); T_mean_11=mean(T(1500:1649,N_dx1)); T_mean_12=mean(T(1650:1799,N_dx1)); T_mean_13=mean(T(1800:1949,N_dx1)); T_mean_14=mean(T(1950:2099,N_dx1)); T_mean_15=mean(T(2100:2249,N_dx1)); T_mean_16=mean(T(2250:2399,N_dx1)); T_mean_17=mean(T(2400:2549,N_dx1)); T_mean_18=mean(T(2550:2699,N_dx1)); T_mean_19=mean(T(2700:2849,N_dx1)); T_mean_20=mean(T(2850:2999,N_dx1)); T_mean_21=mean(T(3000:3149,N_dx1)); T_mean_22=mean(T(3150:3299,N_dx1));

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T_mean_23=mean(T(3300:3449,N_dx1)); T_mean_24=mean(T(3450:3599,N_dx1)); T_mean_25=mean(T(3600:3749,N_dx1)); T_mean_26=mean(T(3750:3899,N_dx1)); T_mean_27=mean(T(3900:4049,N_dx1)); T_mean_28=mean(T(4050:4199,N_dx1)); T_mean_29=mean(T(4200:4349,N_dx1)); T_mean_30=mean(T(4350:4499,N_dx1)); T_mean_31=mean(T(4500:4649,N_dx1)); T_mean_32=mean(T(4650:4799,N_dx1)); T_mean_33=mean(T(4800:4949,N_dx1)); T_mean_34=mean(T(4950:5099,N_dx1)); T_mean_35=mean(T(5100:5249,N_dx1)); T_mean_36=mean(T(5250:5399,N_dx1)); T_mean=[T_mean_1,T_mean_2,T_mean_3,T_mean_4,T_mean_5,T_mean_6,T_mean_7,T_mean_8,T_mean_9,T_mean_10,T_mean_11,T_mean_12... T_mean_13,T_mean_14,T_mean_15,T_mean_16,T_mean_17,T_mean_18,T_mean_19,T_mean_20,T_mean_21,T_mean_22,T_mean_23,T_mean_24... T_mean_25,T_mean_26,T_mean_27,T_mean_28,T_mean_29,T_mean_30,T_mean_31,T_mean_32,T_mean_33,T_mean_34,T_mean_35,T_mean_36]; % Basement temperature T_mi_mean_1=mean(T_mi(1:149,1)); T_mi_mean_2=mean(T_mi(150:299,1)); T_mi_mean_3=mean(T_mi(300:449,1)); T_mi_mean_4=mean(T_mi(450:599,1)); T_mi_mean_5=mean(T_mi(600:749,1)); T_mi_mean_6=mean(T_mi(750:899,1)); T_mi_mean_7=mean(T_mi(900:1049,1)); T_mi_mean_8=mean(T_mi(1050:1199,1)); T_mi_mean_9=mean(T_mi(1200:1349,1)); T_mi_mean_10=mean(T_mi(1350:1499,1)); T_mi_mean_11=mean(T_mi(1500:1649,1)); T_mi_mean_12=mean(T_mi(1650:1799,1)); T_mi_mean_13=mean(T_mi(1800:1949,1)); T_mi_mean_14=mean(T_mi(1950:2099,1)); T_mi_mean_15=mean(T_mi(2100:2249,1)); T_mi_mean_16=mean(T_mi(2250:2399,1)); T_mi_mean_17=mean(T_mi(2400:2549,1)); T_mi_mean_18=mean(T_mi(2550:2699,1)); T_mi_mean_19=mean(T_mi(2700:2849,1)); T_mi_mean_20=mean(T_mi(2850:2999,1)); T_mi_mean_21=mean(T_mi(3000:3149,1)); T_mi_mean_22=mean(T_mi(3150:3299,1)); T_mi_mean_23=mean(T_mi(3300:3449,1)); T_mi_mean_24=mean(T_mi(3450:3599,1)); T_mi_mean_25=mean(T_mi(3600:3749,1)); T_mi_mean_26=mean(T_mi(3750:3899,1)); T_mi_mean_27=mean(T_mi(3900:4049,1)); T_mi_mean_28=mean(T_mi(4050:4199,1)); T_mi_mean_29=mean(T_mi(4200:4349,1)); T_mi_mean_30=mean(T_mi(4350:4499,1)); T_mi_mean_31=mean(T_mi(4500:4649,1)); T_mi_mean_32=mean(T_mi(4650:4799,1)); T_mi_mean_33=mean(T_mi(4800:4949,1)); T_mi_mean_34=mean(T_mi(4950:5099,1)); T_mi_mean_35=mean(T_mi(5100:5249,1)); T_mi_mean_36=mean(T_mi(5250:5399,1)); T_mi_mean=[T_mi_mean_1,T_mi_mean_2,T_mi_mean_3,T_mi_mean_4,T_mi_mean_5,T_mi_mean_6,T_mi_mean_7,T_mi_mean_8,T_mi_mean_9,T_mi_mean_10,T_mi_mean_11,T_mi_mean_12... T_mi_mean_13,T_mi_mean_14,T_mi_mean_15,T_mi_mean_16,T_mi_mean_17,T_mi_mean_18,T_mi_mean_19,T_mi_mean_20,T_mi_mean_21,T_mi_mean_22,T_mi_mean_23,T_mi_mean_24...

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T_mi_mean_25,T_mi_mean_26,T_mi_mean_27,T_mi_mean_28,T_mi_mean_29,T_mi_mean_30,T_mi_mean_31,T_mi_mean_32,T_mi_mean_33,T_mi_mean_34,T_mi_mean_35,T_mi_mean_36]; % Tmr Tmr_mean_1=mean(Tmr(1:149)); Tmr_mean_2=mean(Tmr(150:299)); Tmr_mean_3=mean(Tmr(300:449)); Tmr_mean_4=mean(Tmr(450:599)); Tmr_mean_5=mean(Tmr(600:749)); Tmr_mean_6=mean(Tmr(750:899)); Tmr_mean_7=mean(Tmr(900:1049)); Tmr_mean_8=mean(Tmr(1050:1199)); Tmr_mean_9=mean(Tmr(1200:1349)); Tmr_mean_10=mean(Tmr(1350:1499)); Tmr_mean_11=mean(Tmr(1500:1649)); Tmr_mean_12=mean(Tmr(1650:1799)); Tmr_mean_13=mean(Tmr(1800:1949)); Tmr_mean_14=mean(Tmr(1950:2099)); Tmr_mean_15=mean(Tmr(2100:2249)); Tmr_mean_16=mean(Tmr(2250:2399)); Tmr_mean_17=mean(Tmr(2400:2549)); Tmr_mean_18=mean(Tmr(2550:2699)); Tmr_mean_19=mean(Tmr(2700:2849)); Tmr_mean_20=mean(Tmr(2850:2999)); Tmr_mean_21=mean(Tmr(3000:3149)); Tmr_mean_22=mean(Tmr(3150:3299)); Tmr_mean_23=mean(Tmr(3300:3449)); Tmr_mean_24=mean(Tmr(3450:3599)); Tmr_mean_25=mean(Tmr(3600:3749)); Tmr_mean_26=mean(Tmr(3750:3899)); Tmr_mean_27=mean(Tmr(3900:4049)); Tmr_mean_28=mean(Tmr(4050:4199)); Tmr_mean_29=mean(Tmr(4200:4349)); Tmr_mean_30=mean(Tmr(4350:4499)); Tmr_mean_31=mean(Tmr(4500:4649)); Tmr_mean_32=mean(Tmr(4650:4799)); Tmr_mean_33=mean(Tmr(4800:4949)); Tmr_mean_34=mean(Tmr(4950:5099)); Tmr_mean_35=mean(Tmr(5100:5249)); Tmr_mean_36=mean(Tmr(5250:5399)); Tmr_mean=[Tmr_mean_1,Tmr_mean_2,Tmr_mean_3,Tmr_mean_4,Tmr_mean_5,Tmr_mean_6,Tmr_mean_7,Tmr_mean_8,Tmr_mean_9,Tmr_mean_10,Tmr_mean_11,Tmr_mean_12... Tmr_mean_13,Tmr_mean_14,Tmr_mean_15,Tmr_mean_16,Tmr_mean_17,Tmr_mean_18,Tmr_mean_19,Tmr_mean_20,Tmr_mean_21,Tmr_mean_22,Tmr_mean_23,Tmr_mean_24... Tmr_mean_25,Tmr_mean_26,Tmr_mean_27,Tmr_mean_28,Tmr_mean_29,Tmr_mean_30,Tmr_mean_31,Tmr_mean_32,Tmr_mean_33,Tmr_mean_34,Tmr_mean_35,Tmr_mean_36]; % Ti (internal air) Ti_mean_1=mean(Ti(1:149)); Ti_mean_2=mean(Ti(150:299)); Ti_mean_3=mean(Ti(300:449)); Ti_mean_4=mean(Ti(450:599)); Ti_mean_5=mean(Ti(600:749)); Ti_mean_6=mean(Ti(750:899)); Ti_mean_7=mean(Ti(900:1049)); Ti_mean_8=mean(Ti(1050:1199)); Ti_mean_9=mean(Ti(1200:1349)); Ti_mean_10=mean(Ti(1350:1499)); Ti_mean_11=mean(Ti(1500:1649)); Ti_mean_12=mean(Ti(1650:1799)); Ti_mean_13=mean(Ti(1800:1949)); Ti_mean_14=mean(Ti(1950:2099)); Ti_mean_15=mean(Ti(2100:2249));

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Ti_mean_16=mean(Ti(2250:2399)); Ti_mean_17=mean(Ti(2400:2549)); Ti_mean_18=mean(Ti(2550:2699)); Ti_mean_19=mean(Ti(2700:2849)); Ti_mean_20=mean(Ti(2850:2999)); Ti_mean_21=mean(Ti(3000:3149)); Ti_mean_22=mean(Ti(3150:3299)); Ti_mean_23=mean(Ti(3300:3449)); Ti_mean_24=mean(Ti(3450:3599)); Ti_mean_25=mean(Ti(3600:3749)); Ti_mean_26=mean(Ti(3750:3899)); Ti_mean_27=mean(Ti(3900:4049)); Ti_mean_28=mean(Ti(4050:4199)); Ti_mean_29=mean(Ti(4200:4349)); Ti_mean_30=mean(Ti(4350:4499)); Ti_mean_31=mean(Ti(4500:4649)); Ti_mean_32=mean(Ti(4650:4799)); Ti_mean_33=mean(Ti(4800:4949)); Ti_mean_34=mean(Ti(4950:5099)); Ti_mean_35=mean(Ti(5100:5249)); Ti_mean_36=mean(Ti(5250:5399)); Ti_mean=[Ti_mean_1,Ti_mean_2,Ti_mean_3,Ti_mean_4,Ti_mean_5,Ti_mean_6,Ti_mean_7,Ti_mean_8,Ti_mean_9,Ti_mean_10,Ti_mean_11,Ti_mean_12... Ti_mean_13,Ti_mean_14,Ti_mean_15,Ti_mean_16,Ti_mean_17,Ti_mean_18,Ti_mean_19,Ti_mean_20,Ti_mean_21,Ti_mean_22,Ti_mean_23,Ti_mean_24... Ti_mean_25,Ti_mean_26,Ti_mean_27,Ti_mean_28,Ti_mean_29,Ti_mean_30,Ti_mean_31,Ti_mean_32,Ti_mean_33,Ti_mean_34,Ti_mean_35,Ti_mean_36]; save risultati_cop close all tempo=xlsread('Dati_sperimentali_medie.xls','Tempo','b2:b37'); %% Experimental data % Glass temperature load risultati_cop; sotto=xlsread('Dati_sperimentali_medie.xls','Termocoppia_vetro trasparente','c2:c37'); tt=[1:150:length(T(:,N_dx1))]; plot(11.0833+2*tt/3600,T_mean,'b') hold on plot(tempo,sotto,'o') axis([11 14 0 60]); grid on title('Glass temperature') xlabel('Ore') ylabel('°C') figure % Basement temperature load risultati_cop; sotto=xlsread('Dati_sperimentali_medie.xls','Termocoppia_pavimento','c2:c37'); tt=[1:150:length(T_mi(:,1))]; plot(11.0833+2*tt/3600,T_mi_mean,'b') hold on plot(tempo,sotto,'o') axis([11 14 0 60]); grid on title('Basement temperature') xlabel('Ore') ylabel('°C') figure

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% Tmr load risultati_cop; sotto=xlsread('Dati_sperimentali_medie.xls','Tmr','c2:c37'); tt=[1:150:length(Tmr)]; plot(11.0833+2*tt/3600,Tmr_mean,'b') hold on plot(tempo,sotto,'o') axis([11 14 0 60]); grid on title('Mean Radiant Temperature') xlabel('Ore') ylabel('°C') figure % Ta load risultati_cop; sotto=xlsread('Dati_sperimentali_medie.xls','Ta','c2:c37'); tt=[1:150:length(Ti)]; plot(11.0833+2*tt/3600,Ti_mean,'b') hold on plot(tempo,sotto,'o') axis([11 14 0 40]); grid on title('Internal air Temperature') xlabel('Ore') ylabel('°C')

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