hello every one
tas= 661.M.sqrt theta with theta=T\Ts T=(273+sat°c )K Kelvin & Ts=288K(273+15°c)
to find this formula:
tas=M.a & a square=k.R.T k=1.4 for dry air =cte
R(universal gas cte)=287joules\kg & K
T=temperature in kelvin
now take above formula & multiply & divide at the same time by a0=speed of sound at sea level=661kts.
so: tas=ao.M.squareroot of k.R.T\squareroot of k.R.Ts
a0square being of course=k.R.Ts
theta=k.R.T\k.R.Ts=T\Ts
so finally: tas=661.M.sqrt theta
equally eas=661.M.sqrt delta with delta=p\po p=atm pressure in Hpa & po=1013.25Hpa
delta=sigma x theta ; sigma=rho(density in kg\m3)\rhozero
rhozero=1.225kg\m3
to find above formulas think of mr boyle's gas laws: p=rho.R.T & po=rhozero.R.Ts divide both formulas & find: p\po=rho\rhozero x T\Ts
thus: delta=sigma x theta
conclusion: tas=function of mach & temperature whereas ias & eas are function of mach & pressure
so we see it every day in climb:
first climb at cte eas, mach increases & theta decreases
then at crossover altitude climb at cte mach & eas & delta now decreases.
stop here before my headache starts again