ias as a function of hp derivation
a=26.38761
b=1.33E-07
hp=(a/IAS+b*IAS^3)
This is a quartic of the form*
b*ias^4-hp*ias+a=0 or x^4-(hp/b)*x+a/b=0
This is already in a reduced form which allows solving for a resolvent cubic*
x^3 - (a/(4*b))*x - (hp/b)^2/64
where the 2 real roots (x1,x2) in the original quartic are combinations of the 3 roots (l,m,n) from the cubic.
x1=(l^.5+m^.5+n^.5) x1 is the front side of the power curve
x2=(l^.5-m^.5-n^.5) x2 is the ?back? side of the power curve, (I still need to understand this root better).
tmp=(hp/b)^4/16384-(a/(12*b))^3
if tmp < 0, this indicates not enough horsepower for straight and level flight.
A=(((hp/b)^2/128)+tmp)^(1/3)
B=(((hp/b)^2/128)-tmp)^(1/3)
l=(A+B)^.5
m=-.5*(A+B)+i*sqrt(3)/2)*(A-B)
n=-.5*(A+B)-i*sqrt(3)/2)*(A-B)
Since these are complex entities and since we are only interested in real results the sum of m and n
or the negate of the sum of m and n are the only roots we want to look at (this is why I don't even
bother with x3 and x4)
theta=(PI-arctan(sqrt(3)*(A-B)/(A+B)))
mrad=(.25*(A+B)^2+.75*(A-B)^2)^.5
real(m^.5)=COS(theta/2)*(.25*(A+B)^2+.75*(A-B)^2)^.25
real(n^.5)=same as real(m^.5)
imaginary parts of m^.5 and n^.5 are the same with opposite sign and are ignored.
x1=ias=l+m+n
x1=ias=(l^.5+m^.5+n^.5) x1 is the front side of the power curve
From pgs 8 & 9 of "Handbook of Mathematical Tables and formulas" Burington 3rd edition Copyright 1948
Tim Corrie (timc@microsoft.com)