Many different quantities in aerospace engineering depend on the temperature, pressure, and density of the atmosphere at the current altitude. The atmosphere can be modeled as a series of alternating isothermal and gradient regions. Within the gradient region, the temperature (T), pressure (p), and density () are defined by the following equations: where a is lapse rate for the region in oR/ft, R is the specific gas constant of 1716 (ft*lbf)/(slug* oR), g0 is the acceleration due to gravity of 32.2 ft/s2, and h represents the geopotential altitude in ft. The subscript 1 indicates that the value of the parameter is 2 from the base of the region. The first gradient region in the atmosphere begins at sea level (0 ft), where T = 518.69 oR, p = 2116.2 lbf/ft2, and = 0.002377 slug/ft3, and ends around 36089 ft. See the document The Standard Atmosphere under References on Blackboard for more information. Write a program that will 1. Ask the user for the geopotential altitude, the lapse rate, and the base values for altitude, temperature, pressure, and density for the current gradient region 2. Calculate the temperature, pressure, and density at the specified altitude (NOTE: Write this task as a function.) 3. Display the results to the command window.

T= T1+a(H-H1)

P/P1=(T/T1)^(-go/aR)

P/P1=(T/T1)^-((go/aR)+1)

One example of running this program is:

Enter the current altitude (ft) :14500

Enter the lapse rate (deg Rankine/ft) :-3.566*10^-3

Enter the base altitude for the region (ft): 0

Enter the base temperature (deg Rankine) :518.69

Enter the base pressure (lbf/ft^2): 2116.2

Enter the base density (slug/ft^3): 0.002377

At a geopotential altitude of 14500.00 ft, the temperature is 466.98 deg R, the pressure is 1217.78 lbf/ft^2, and the density is 0.0015 slug/ft^3.