True Airspeed question??????

[wessidemike]

sorry for posting here, but i figured you guys would be the closest to CFI's as i could get.

An aircraft is flyign at a constant power setting and constatn indicated altitude. If the OAT decreases true airspeed will.


A. decrease and true alt will decrease
b. Increase and true alt will increase
c. increase and true alt will decrease


answer is A but why. i understand the true alt part, but the true airspeed i do not. If temp is decreasing then density alt is decreasing. doesnt' a lower density alt incrase aircraft performance? why does airspeed decrase. i though as air becomes colder it becomes more dense and then would have more molicules to cram into the pitot tube.

 

[bandit110]

sorry for posting here, but i figured you guys would be the closest to CFI's as i could get.

An aircraft is flyign at a constant power setting and constatn indicated altitude. If the OAT decreases true airspeed will.


A. decrease and true alt will decrease
b. Increase and true alt will increase
c. increase and true alt will decrease


answer is A but why. i understand the true alt part, but the true airspeed i do not. If temp is decreasing then density alt is decreasing. doesnt' a lower density alt incrase aircraft performance? why does airspeed decrase. i though as air becomes colder it becomes more dense and then would have more molicules to cram into the pitot tube.

You just answered the question. Got colder, got denser, now less gap between TAS and IAS = lower TAS

 

[Mel Sharples]

Wow... I'm surprised you don't know this. It is very basic math.

The energy equation for adiabatic flow of an ideal gas is this where v is the flow velocity and h is the specific enthalpy. This implies that if a flow with free stream velocity v0 and enthalpy h0 is brought to rest adiabatically, and if h1 is the enthalpy of the resting gas, then you have this.

Also, for an ideal gas we have dh/dT = cp, where the specific heat cp is essentially constant for relatively small changes in temperature, so this equation can be written as this.

​

Now, the speed of sound in an ideal gas is given by this equation where g = cp/cv is the ratio of specific heats and R is the gas constant, so we can express any given temperature T in terms of the speed of sound at that temperature. With these substitutions, the preceding equation becomes this.

Also, for an ideal we have R = cp - cv, so we can make this substitution, divide through by a02, and re-arrange terms to give us this.​

The ratio v0/a0 is, by definition, the Mach number M of the free stream, and since temperature is proportional to the square of the speed of sound, the ratio (a1/a0)2 equals the ratio of temperatures T1/T0. Hence we have this.

​

Furthermore, using the ideal gas equation p = rRT we can substitute for the temperatures to give us this.


As discussed in The Speed of Sound, for an adiabatic quasi-static (i.e., isentropic) process, the ratio p/rg is constant. Thus if we re-write the above equation as this, the first factor on the left side is unity, and we arrive at the formula for the isentropic pressure rise of an ideal fluid being brought to a stop from a Mach number M here. Solving this equation for M and then multiplying through by the freestream speed of sound like this, we have the formula for the true airspeed vtrue = v0 as a function of the freestream static pressure p0, the total (stagnation) pressure p1, and the freestream static temperature T0 like this.

Now this is all off the top of my head. If you want a more in depth answer, I will have to sit down and work a few more equations. You probably want to have this page memorized prior to your CFI checkride.


NOTE: Of course I am kidding about this... the previous post was about all you need to know! Just having a little fun with you. Good luck!

 

[Mel Sharples]

i understand the true alt part, but the true airspeed i do not. If temp is decreasing then density alt is decreasing. doesnt' a lower density alt incrase aircraft performance? why does airspeed decrase. i though as air becomes colder it becomes more dense and then would have more molicules to cram into the pitot tube.

The air is "thinner" when it is warmer. Therefore, you have to go faster to get the same indicated airspeed when it is warmer as it was when it was colder. Like you said, fewer molecules means you have to go faster to get the same IAS. To go faster to get the same IAS means a higher TAS.