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Have a look at the following performance charts from Section 5 of Robinson R-22 Pilots Operating Handbook for hover out of ground effect (HOGE). If the temperature and gross weight are known, the hover ceiling of the helicopter can be determined through these charts:

Three performance charts from R-22 POH

The feature all three charts have in common is a 'knee' - a sudden change in the gradient of the slope. But why is that? Why do the slopes get steeper beyond a particular gross weight?

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    $\begingroup$ @AdityaSharma- I suspect a "knee" is a line that increases sharply and then at some point changes slope to something less steep. Like a leg bent at the knee. $\endgroup$
    – Jim
    Dec 23, 2022 at 2:15
  • $\begingroup$ This is conjecture but isn’t there a governor point at which you are maxed out on engine HP and rotor RPM, and any further weight increase must be accommodated solely by altitude loss? Also, it made me wonder if you’re torque limited in those zones to protect tail rotor effectiveness. $\endgroup$
    – Max R
    Dec 23, 2022 at 3:08
  • $\begingroup$ @MaxR: you might be right. Gearbox is also normally torque limited. $\endgroup$
    – sophit
    Dec 23, 2022 at 13:27

2 Answers 2

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The knee is a result of having the engine "flat rated", that is rated to a power limit that is below its potential wide open throttle horsepower at sea level, a very common practice with helicopters. The Lycoming O-360 engine it has is normally rated at 180 HP when used on regular airplanes (wide open throttle at sea level).

To give the helicopter flexibility in altitude performance, they arbitrarily limit its power at lower altitudes to hold back some "in reserve" you might say. That is flat rating.

The R-22 is derated to 131HP at sea level and up to its critical altitude even though its displacement makes it technically capable of making 180 HP. Below critical altitude, you will be less than WOT, observing a redline on the manifold pressure gauge (24.5 inches of MP, whereas WOT will be around 29-30) that sets the 131HP limit. At the critical altitude, you will be at redline with WOT and the engine making 131HP, and HP available declines with altitude above that.

The slope of the curve is the gross weight limitation with altitude for HOGE at a range of temperatures. The steep part of the slope represents the reduction in GW imposed by aerodynamic factors unrelated to engine horsepower. Then you get to the critical altitude, where you are now at WOT to just make the manifold pressure redline, and the decline in power with altitude increases the decline in allowable gross weight.

So, the knee in the curve is the point at which the critical altitude is reached at different temperatures for the particular configuration depicted in the chart.

You also have a kind of unofficial "emergency reserve" available if you really got yourself in trouble below critical altitude, but you have to remember the transmission/rotor are designed for 131 HP and you'll overstress the transmission system and rotor by using WOT in some kind of rescue-yourself-or-die situation that takes the engine past 24.5" of manifold pressure. Not sure how the manual handles that, but owner will be unhappy with you if it affects the life of the transmission/rotor and they find out, but better than crashing.

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  • $\begingroup$ Very good answer. Maybe you can add that the engine could be derated also due to gearbox limitations and it makes lose some payload at low altitude. $\endgroup$
    – sophit
    Dec 23, 2022 at 16:32
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    $\begingroup$ Thanks. Well they'll design the gearbox for the horsepower the machine is designed for regardless. The fact that the engine is derated isn't really relevant. The machine and its gearbox is designed to handle 131 HP. They could just put a Lyc O-290 in it, un-derated and have the same sea level performance with that gearbox. $\endgroup$
    – John K
    Dec 23, 2022 at 16:52
  • $\begingroup$ Added some extra in response to your comment. $\endgroup$
    – John K
    Dec 23, 2022 at 17:00
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    $\begingroup$ Another bonus is, an O-360 that never has to make more than 131 HP is so under stressed it could probably run 4000 hours to overhaul. When it gets to the 2000 hr rebuild after a few years of steady regular operation, the inside of the engine will be pristine. $\endgroup$
    – John K
    Dec 23, 2022 at 20:28
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    $\begingroup$ Not RPM limited. These things run at or near redline RPM full time. Just the point at which it takes wide open throttle just to get 24.5" of manifold pressure, the limit for the derated engine. So power available is constant up to the critical alt, b/c you can keep opening the throttle to maintain 24.5". Above critical altitude, wide open throttle is LESS than 24.5", declining as you go up. $\endgroup$
    – John K
    Dec 24, 2022 at 5:29
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There is something in section 7-4 about using the collective above a certain altitude to maintain rpm once the engine is maxed out on power.

The steep part of the weight vs maximum hover altitude curve indicates performance is based on the (collective) rotor pitch at an Angle of Attack matching the engines power output while maintaining constant rotor rpm. The decrease in rate of lifting capacity is consistent with exponentially increasing Drag and increased rotor interference as rotor AoA increases.

at the "knee" the engine is at full throttle and the rotor blade is at optimal AoA (maximum Lift/Drag ratio) at maximum allowable RPM

Above a certain (density) altitude decreasing Wide Open Throttle engine power output at constant rpm means rotor blade pitch is further reduced to maintain rpm. But rate of loss of maximum hover altitude as weight increases is not as steep because rotor Lift to Drag ratios are more favorable and rotor interference turbulence is reduced.

Another way of looking at the "knee" concept would to mount a large rotor on a tiny motor. It could only spin a constant rpm up to a limited AoA before the engine simply could not give any more power. The point at which AoA cannot be increased any more is the "knee". Really a wall.

Now, take a tiny rotor on a very large motor. AoA could be increased until until the blade stalled, resulting in a straight line of lift increase, then a sharp decrease.

Practically, matching helicopter motors with rotors tries to avoid both extremes, erring on the side of limiting engine power. Under conditions of manifold pressure limitation or "hot/high" air density, the knee will show up on the graphs.

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