# Temperature, Range and Endurance

#### chris

##### Well-Known Member
Hey guys,

Can someone please explain the relationship between temperature and range/endurance?

I could have sworn I read in the Jepp Comm book that as temps decrease, both range and endurance increase; however, in my Seminole POH, it is the opposite (it says to increase range 1nm for each degree celcius above std, and to decrease it 1.5nm for each degree celcius below std).

I beleive it might have to do with induced drag--air is thicker at colder temps and causes more drag=less endurance/range. I could be way off though. just a quess.

Engines produce mopre power the colder it is, but that is marginal considering the much reduced drag as it gets warmer

Colder air is more dense than hot air. If you have two equal volumes of air (roughly the size of an engine's cylinders), the cold air will have more mass than the warm air.

More air also means more fuel is required to keep a stoichiometric air/fuel ratio. Fuel has a fixed amount of energy available per mass (specific energy), so with a more massive fuel/air mix available for combustion, you'll be producing more power.

The tradeoff is that that available power increase doesn't come from thin air (thick air?). Fuel massflow rates for a given engine speed will be higher in cold air as well. This is where that reduction in range can come from.

[ QUOTE ]
Hey guys,

Can someone please explain the relationship between temperature and range/endurance?

I could have sworn I read in the Jepp Comm book that as temps decrease, both range and endurance increase; however, in my Seminole POH, it is the opposite (it says to increase range 1nm for each degree celcius above std, and to decrease it 1.5nm for each degree celcius below std).

[/ QUOTE ]

First an overview of best range and best endurance for reciprocating engine powered propeller aircraft.

Best range is found at L/D max. This is the indicated airspeed at which you have the least amount of drag for the highest amount of lift. Since drag is lowest at this speed, the least amount of thrust is required (remember thrust = drag in level flight). It is also the airspeed for best glide. For a recip. powered airplane flown at the correct IAS for L/D max, density altitude should have little to no effect on range. This may seem strange, as we know that as altitude increases, TAS will increase for a given IAS. But, at higher altitudes as TAS increases the power required to maintain them is also increased, even though drag remains constant. Remember that power is a rate at which work is done, if we are going faster, then more power is required. Since drag is not increased, the amount of power required is directly proportional to the increase in speed. So if our TAS is 10% higher than IAS, we theoretically need 10% more power. Any variation in specific range (specific range = NM / lbs. of fuel) with altitude is strictly a function of engine-propeller performance.

Best endurance is found at a slower speed than best range. It corresponds to the speed where the least amount of power is required to maintain altitude. For a rule of thumb it is about 75-76% of the speed for L/D max. Usually best endurance is just above stall. For the Piper Cadet with a best glide of 73 KIAS, we can estimate best endurance of 55 KIAS. Unlike best range, best endurance is dependent on altitude. Best endurance is found at sea level. Best endurance, like best range is found at the same IAS regardless of altitude. We know the power required to maintain a given IAS increases with density altitude (since more work is being done), and more power = more fuel flow. So, the lower the better. Since we want the lowest density altitude possible, the effects of temperature are obvious.

The best way to find the speed for best endurance would be to slow down by slowly reducing power until an airplane will just hold altitude. This should give you the least fuel flow.

It may seem strange that the speed which requires the least thrust is different from the speed that requires the least power. But, power and thrust are not the same. Thrust is a pushing force and power is the rate work is done.

The problem with the charts in the Seminole POH, is that they do not actually give you the speeds for best power and best endurance. They give three power settings, all of which are far too high for either condition. This makes it a lot harder to see what is really going on.

Assuming you use the correct speed for best range, temperature and pressure will have no effect on max range, as long as the correct speed can be maintained. The Seminole POH assumes just setting a power and taking what you can get. In this situation, if you just want to set a certain power like 75%, then best range will occur at the altitude with the highest TAS for that power setting. This will occur at the highest density altitude where 75% power can be maintained. If we increase the temperature, then density altitude increases, the spread between TAS and IAS increases, and maximum range increases. If you want true maximum range, then a speed between Vx and Vy would give best range. In practice Vy would be a good choice. It is normal in long-range cruise to pick a speed slightly higher than optimum to pick up a few knots in exchange for a very small range penalty. You would also want to pick the highest MAP and lowest RPM possible (within allowable limitations).

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