Air Density at Altitude
PROBLEM: PSAS seeks to design rocket control fins that will facilitate guidance of an amateur rocket. With the success of the roll-control system, it is assumed that the main fins can be angled in a similar fashion to steer the rocket on a desired trajectory. To maintain stability, we must be able to predict the forces produced by the fins in flight. Then, when a desired amount of fin force is needed for control, the fins can be angled to produce that force. The fin forces will depend on air density.
GIVEN: Height above standard sea level, h.
REQUIRED: Determine (a) air temperature at various altitudes, (b) air pressure at various altitudes, (c) air density at various altitudes. Calculate parts a-c for 750 meters above standard sea level.
EQUATIONS:
(a)
T(h)=15.04-0.00649*h+273.1 for h<11000
T(h)=-56.46+273.1 for 11000≤h<25000
T(h)=-131.21+0.00299*h+273.1 for h≥25000
(b)
p(h)=101.29*[T(h)/288.08]^5.256 for h<11000
p(h)= 22.65e^((1.73-0.000157h) ) for 11000≤h<25000
p(h)= 2.488*[T(h)/216.6]^(-11.388) for h≥25000
(c)
ρ=p(h)/(0.2869*T(h))
All of the equation above comes from NASA’s website ("Earth Atmosphere Model").
CALCULATIONS:
(a)
T(750)=15.04-0.00649*(750)+273.1 = 283.273 K
(b)
p(750)=101.29*[283.273/288.08]^5.256 = 92.7154 KPa
(c)
ρ=(92.7154 KPa)/(0.2869*283.273 K) = 1.14 kg/m^3
GRAPH:
Below is a graph of air temperature at various altitudes.
Below is a graph of air density at various altitudes.
WORKS CITED
Earth Atmosphere Model. , www.nasa.gov. Web. 12 May 2011.
<http://microgravity.grc.nasa.gov/education/rocket/atmosmet.html>.