14.5 Is there some sort of equation to figure out true airspeed (TAS)?

From FlightSim

There is no easy solution to this since the equation is complicated due to the effects of density, compressibility etc and it is nonlinear.

Practical solution till 10000 ft is

                            TAS = IAS+ (1.75% of IAS per 1000ft altitude)

This is as per Ground Studies for Pilots.

A more detailed formula can be used if you employ a pocket calculator/ computer...

Where T = temp in deg celsius, B = IAS in kts, z=height in ft,Then

    z' = (0.001*z)/3.281
 
    T' = T+273
 
    P  = 1013.25*((1-0.022558*z') raised to the power 5.25611)
 
    TAS = B*( square root of(1013.25*T'/(P*288.15))
 
    M No =  (TAS*0.0256)/square root of T'

Once you have finished rolling down the floor with mirth at my woeful attempt to replace by words the math symbols which I am unable to find immediately, you may try them for size.

Bala

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I'm not sure if this will help, but I'll chuck it in anyway (cut and pasted from a reference page from somewhere on the net):

Density altitude example:

Let pressure altitude (P_alt) be 8000 ft, temperature 18C.

Standard temp (T_s) is given by

   T_s=15-.0019812*8000=-0.85C = (273.15-0.85)K=272.3K

Actual temperature (T) is

 18C=(273.15+18)K=291.2K

  Density altitude (D_Alt) = 8000 + (272.3/.0019812)*(1-(272.3/291.2)^.23498)
                          = 8000 + 2150=10150ft 

or approximately:

 Density Altitude=8000 + 118.6*(18+0.85)=10236ft

Relationship of true and calibrated (indicated) altitude:

TA= CA + (CA-FE)*(ISADEV)/(273+OAT)
  

where

TA= True Altitude above sea-level
FE= Field Elevation of station providing the altimeter setting
CA= Calibrated altitude= Altitude indicated by altimeter when set to the
      altimeter setting, corrected for calibration error.
 
ISADEV= Average deviation from standard temperature from standard in the air
column between the station and the aircraft (in C)
 
OAT= Outside air temperature (at altitude)

The above is more precise than provided by the E6B or similar.

.. end of quote ...

Ian Donohoe

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This whole calc is based on the following.....

 First  Sea Level density = 1.2256
        Gas Const  R =2.8704
        Temp used is in Kelvin ie T+273 deg in celsius
        1 metre=3.281 ft
        Pressure measured in mb
 
 
        Till 36089 ft,
 
                       Amb Pressure/SL Pressure=(Amb Temp/SL Temp)^5.25588
 
                       Amb Density/SL Density  =(Amb Temp/SL Temp)^4.25588
 
        Above 36089 ft,
 
                       Amb Density/SL Density  = 0.297076*e^(-(z-36089.24)/20805.8)
 
        TAS = IAS*(SL Density/Amb Density)^0.5
 
        (SL Density/Amb Density)^0.5 = ((SL Press*Amb Temp)/(Amb Press*SL Density))^0.5                        
  Then Ambient Density=Ambient Pressure/(R*Ambient Temp in Kelvin)
        
       TAS = IAS*(Sea Lvl Density/Ambient Density)^0.5
 
 
       Amb Pressure  = 1013.25(1-0.022558*z)^5.25611     where z=ht in kms
                                                    

So, utilising the above info and invoking few magical chants, we can arrive at

Where T = temp in deg celsius, B = IAS in kts, z=height in ft, then

    z' = (0.001*z)/3.281
 
    T' = T+273
 
    P  = 1013.25*((1-0.022558*z') ^ 5.25611)
 
    TAS = B*( square root of(1013.25*T'/(P*288.15))
 
    M No =  (TAS*0.0256)/squareroot of T'

bala