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Rocket Man

Rocket Man. ME 340 Final Project Bryan Johnson, Devin LeBaron. Introduction. The Problem. How close could a spaceship fly to the sun before melting?. The Sun. Temp = 5800 K Radius = 6.95e8 m Assume blackbody ( ε =1). The Space Ship. Assume Aluminum body Melting Temp = 933 K

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Rocket Man

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  1. Rocket Man ME 340 Final Project Bryan Johnson, Devin LeBaron

  2. Introduction

  3. The Problem • How close could a spaceship fly to the sun before melting?

  4. The Sun • Temp = 5800 K • Radius = 6.95e8 m • Assume blackbody (ε=1)

  5. The Space Ship • Assume Aluminum body • Melting Temp = 933 K • To approximate the shape… • We will use a sphere

  6. Energy Balance In space, convection and conduction don’t apply • E*As αGs*Ac Ac = πD^2/4 As = πD^2 E*As = αGs*Ac εσT^4*As = αGs*Ac εσT^4 = αGs/4 Gs = 4εσT^4/α Space Ship

  7. Emissivity and Absorptivity At Tm = 933 K: F1 = 0.4301; F2 = 0.9628 ε(Tm) = 0.2(0.4301) + 0.9(0.9628 - 0.4301) + 0.35(1 – 0.9628) ε(Tm) = 0.58 • Chart based on graph from Fig 12.17 from the book At Ts = 5800 K: F1 = 0.9904; F2 = 0.9998 α(Ts) = 0.2(0.9904) + 0.9(0.9998 - 0.9904) + 0.35(1 - 0.9998) α(Ts) = 0.2066

  8. Radiation of the Sun Ab • qs = Es*As • qs = σT^4*As • qs = Gs*Ab • Gs*Ab = σT^4*As • Gs = σT^4*As/Ab • Gs = σT^4*Rs^2/(D+Rs)^2 Ship D As

  9. Combine the formulas • Gs = σTs^4*Rs^2/(D+Rs)^2 • Gs = 4εσTm^4/α • 4εσTm^4/α = σTs^4*Rs^2/(D+Rs)^2 • Solving for D: • D = [(αTs^4*Rs^2)/(4εTm^4)]^.5 – Rs ε = 0.58 α = 0.2066 Tm = 933 K Ts = 5800 K Rs = 6.95e8 m D = 7.32e9 m

  10. The Answer • The final distance to melting your aluminum space ship would be about: • 7.32e9 m = 4,550,000 miles Mercury is about 5.8e10 m from the sun. Which means you’d be pretty darn close.

  11. Conclusions and Recommendations • What are you doing flying to the sun? Just don’t. But if you must, please use a better material with a higher melting point, better heat resistance and lower absorptivity.

  12. References • Incropera, Frank P., and Frank P. Incropera. Fundamentals of Heat and Mass Transfer. Hoboken, NJ: John Wiley, 2007. Print. • Rocketman. Perf. Harland Williams, Jessica Lundy, and William Sadler. Disney, 1997.

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