To meet the Army High-Hot standard (4,000 ft, 95 degF) you have to prove that you can hover out-of-ground-effect (OGE). For Army standards you also must have a 500 ft/min rate of climb capability. For hand calculations follow this format:
1. Get Power available @ altitude
a. P_avail(alt)=0.90*P_avail(sea-level)*density(alt)/density(sea-level)
Note: The 0.90 term is to account for fuselage downwash, but varies between rotorcraft.
2. Determine profile and induced power for both the main rotor and tail rotor. Since the aircraft is in hover flight, the fuselage parasitic power will be zero.
a. Vinduced(hover,const alt)=sqrt(TOGW/(2*density(alt)*Area(Main Rotor)))
Note: 2.a only works in hover at constant altitude.
b. Pinduced=1.15*TOGW*Vinduced
Note: 1.15 is an empirical correction factor.
c. Cprofile(hover)=Cd0*solidity(MR)/8
d. Pprofile(hover)=density(alt)*Area(MR)*tipspeed^3*Cprofile(hover)
Warning: Make sure your units are right!!! If you are working in english units make sure to convert to HP (1 HP=550 ft-lbs/sec).
3. Sum Pinduced and Pprofile, then divide it by the angular velocity of the main rotor, which gives you the torque of the main rotor.
4. To determine the thrust of the tail, divide the main rotor torque by the distance between rotor centers (can be found in Janes AWA).
5. Use the tail thrust instead of TOGW in equations 2.a and 2.b, and wherever you see MR replace with tail rotor (TR), then repeat the equations above to determine the total power required in the tail.
6. Prequired=Prequired(MR)+Prequired(TR)
You may want to divide Prequired by 0.95 to account for transmission losses.
7. R/C(ft/min)=(Prequired(ft-lbs/sec)-Pavail(ft-lbs/sec))/TOGW(lbs)*60sec/1min
If rate of climb (R/C) is 500 ft/min or higher, then your helicopter will meet the Army high-hot conditions. Good luck, and pay close attention to your units!!!