Best lift/drag speed question
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Best lift/drag speed question
Hi everyone,
Been having a little argument over what is the best lift/drag ratio speed in a C152.
Just quickily to re-cap, best L/D speed is usually at an angle of attack of 4 degrees, correct? Cessna manual gives the best glide speed at 60kts, which we can assume is at 4 degrees, for the best lift/drag ratio(max glide range).
Problem is I'm told that 60 kts is also the best lift/drag ratio speed for level flight. This I can't understand.
Firstly in a glide, the path travelled of the AC is downwards, so the relative airflow is opposite(coming from below as well as in front). Where in straight and level the relative airflow is from directly ahead. This would affect the way the wing produces lift.
Any also just thinking about it logically, aircraft are designed to crusie at around 4 degrees angle of attack, so one would think the best L/D ratio speed would be around 95 to 100kts? Think about the nose attitue you would have flying straight and level at 60kts, surely the angle of attack must be higher than 4 degrees.
Cheers,
Stefan
Been having a little argument over what is the best lift/drag ratio speed in a C152.
Just quickily to re-cap, best L/D speed is usually at an angle of attack of 4 degrees, correct? Cessna manual gives the best glide speed at 60kts, which we can assume is at 4 degrees, for the best lift/drag ratio(max glide range).
Problem is I'm told that 60 kts is also the best lift/drag ratio speed for level flight. This I can't understand.
Firstly in a glide, the path travelled of the AC is downwards, so the relative airflow is opposite(coming from below as well as in front). Where in straight and level the relative airflow is from directly ahead. This would affect the way the wing produces lift.
Any also just thinking about it logically, aircraft are designed to crusie at around 4 degrees angle of attack, so one would think the best L/D ratio speed would be around 95 to 100kts? Think about the nose attitue you would have flying straight and level at 60kts, surely the angle of attack must be higher than 4 degrees.
Cheers,
Stefan
Join Date: Feb 2007
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The AOA for minimum drag (i.e. best L/D) is not affected by flight path angle, so whether you are gliding, in level flight or climbing it will be the same. That translates to the same airspeed, for a given weight. 60 knots in this case according to Cessna, who should know these things.
You are confusing angle of attack, pitch angle and flight path angle. Assuming the wing incidence is zero:
Pitch Angle = Flight Path Angle + AOA
In level flight, flight path angle is zero so for minimum drag speed of 60 kts, which you assumed to be an AOA of 4 deg, pitch will also be 4 degrees. In a 5 degree glide at 4 degrees AOA, the pitch angle will be 1 degree nose down. A climb angle of 5 degrees with AOA of 4 deg means pitch angle will be 9 deg. In all three cases IAS will be 60, and the wing will be at maximum L/D. Only the power setting will be different.
Minimum drag speed is not usually the optimum cruising speed, however. You will stay aloft for a long time, but won't get very far. Cruising speeds are set higher so range is optimised.
In other words, aircraft are not designed to cruise at L/D max, but much faster.
You are confusing angle of attack, pitch angle and flight path angle. Assuming the wing incidence is zero:
Pitch Angle = Flight Path Angle + AOA
In level flight, flight path angle is zero so for minimum drag speed of 60 kts, which you assumed to be an AOA of 4 deg, pitch will also be 4 degrees. In a 5 degree glide at 4 degrees AOA, the pitch angle will be 1 degree nose down. A climb angle of 5 degrees with AOA of 4 deg means pitch angle will be 9 deg. In all three cases IAS will be 60, and the wing will be at maximum L/D. Only the power setting will be different.
Minimum drag speed is not usually the optimum cruising speed, however. You will stay aloft for a long time, but won't get very far. Cruising speeds are set higher so range is optimised.
In other words, aircraft are not designed to cruise at L/D max, but much faster.
The mistake you are making is confusing angle of attack with attitude.
Angle of attack is angle between the chord line and the relative airflow, not the local horizontal. If the aircraft is heading straight down, the relative airflow is straight up, if heading straight up, the airflow is straight down.
In a glide, the relative airflow is from a small downward angle in front of the aircraft. fly with the chord line at your 4deg to that flow and you have your best L/D. This will NOT be an attitude of 4deg, it would be slightley lower.
Also must say, 60kts could only be speed for best l/d at a particular weight. The actual speed for best L/D will be higher at high weights and lower at low weights.
Angle of attack is angle between the chord line and the relative airflow, not the local horizontal. If the aircraft is heading straight down, the relative airflow is straight up, if heading straight up, the airflow is straight down.
In a glide, the relative airflow is from a small downward angle in front of the aircraft. fly with the chord line at your 4deg to that flow and you have your best L/D. This will NOT be an attitude of 4deg, it would be slightley lower.
Also must say, 60kts could only be speed for best l/d at a particular weight. The actual speed for best L/D will be higher at high weights and lower at low weights.
For a piston engine (which one can call a power producing engine) the interesting speeds can be derived from the power required curve. For a turbo-jet engine (a thrust producer) you would use the thrust required curve or, to call it by a different name, the total drag curve.
Both curves have similar though different inverted U shapes and use TAS along the x-axis. They use different units for the y axis (power and drag, naturally).
You can see examples of these curves at:
http://www.allstar.fiu.edu/AERO/BA-Form&gra.htm
They are near the bottom of the page after all the frightening looking maths equations!
The curve of speed against power required has two interesting points:
1. The bottom of the curve shows the speed where power required is at a minimum. This speed will give minimum fuel flow i.e. max endurance. It will also give minimum sink speed for gliding and be very close to the speed for best climb angle.
2. The tangent to the curve from the origin will show the speed where the ratio of speed to power is at a maximum. Now, as power is equal to drag times speed, it can be shown by clever mathematics that this tangent also defines the minimum drag speed, or best L/D speed. That speed will give the best range, the best gliding angle and be close to the speed for best climb rate.
The curve is for a particular airframe and propeller configuration at a given weight.
So, for a Cessna 152, if the speed for best gliding angle is at 60kts, that speed will give the best L/D ratio for the aircraft gliding with the propeller windmilling. If the propeller is producing thrust, the L/D ratio will be improved at 60kts and you can fly a little faster before the drag and power required increases to the point where the ratio of speed to power is once again at a maximum. In other words, you have drawn a new power required curve because you have changed the configuration from a draggy windmilling prop to a prop doing some useful work.
That is why the best L/D speed is different at different power settings.
So if Cessna state that the best gliding speed is 60kts, that doesn't necessarily mean that the best range speed is also 60kts. It will be faster. But it's true that the normal cruise speed of say, 90kts, will be faster than that for best range. We accept the compromise that for a slightly increased fuel consumption, we can get a quicker flight time.
If you are critically short of fuel, you will get better range in still air, or with a tailwind, if you slow down. The wind component will have a large effect on the chosen speed, such that in a strong headwind, you may be better off actually increasing speed!
For a turbo-jet, the interesting curve is that of speed against total drag, but that's not the subject of your question!
Both curves have similar though different inverted U shapes and use TAS along the x-axis. They use different units for the y axis (power and drag, naturally).
You can see examples of these curves at:
http://www.allstar.fiu.edu/AERO/BA-Form&gra.htm
They are near the bottom of the page after all the frightening looking maths equations!
The curve of speed against power required has two interesting points:
1. The bottom of the curve shows the speed where power required is at a minimum. This speed will give minimum fuel flow i.e. max endurance. It will also give minimum sink speed for gliding and be very close to the speed for best climb angle.
2. The tangent to the curve from the origin will show the speed where the ratio of speed to power is at a maximum. Now, as power is equal to drag times speed, it can be shown by clever mathematics that this tangent also defines the minimum drag speed, or best L/D speed. That speed will give the best range, the best gliding angle and be close to the speed for best climb rate.
The curve is for a particular airframe and propeller configuration at a given weight.
So, for a Cessna 152, if the speed for best gliding angle is at 60kts, that speed will give the best L/D ratio for the aircraft gliding with the propeller windmilling. If the propeller is producing thrust, the L/D ratio will be improved at 60kts and you can fly a little faster before the drag and power required increases to the point where the ratio of speed to power is once again at a maximum. In other words, you have drawn a new power required curve because you have changed the configuration from a draggy windmilling prop to a prop doing some useful work.
That is why the best L/D speed is different at different power settings.
So if Cessna state that the best gliding speed is 60kts, that doesn't necessarily mean that the best range speed is also 60kts. It will be faster. But it's true that the normal cruise speed of say, 90kts, will be faster than that for best range. We accept the compromise that for a slightly increased fuel consumption, we can get a quicker flight time.
If you are critically short of fuel, you will get better range in still air, or with a tailwind, if you slow down. The wind component will have a large effect on the chosen speed, such that in a strong headwind, you may be better off actually increasing speed!
For a turbo-jet, the interesting curve is that of speed against total drag, but that's not the subject of your question!
headwinds vs. maximum range
eckhard stated "The wind component will have a large effect on the chosen speed, such that in a strong headwind, you may be better off actually increasing speed!"
I once did the exercise of reading off best fuel consumption / speeds from the C172 POH curves and entered the figures against various headwinds into a table, to see how the range was affected by headwinds. (Can't find the spreadsheet....!) The result surprised me, with maximum range consistently being achieved with the still-air-most-economic-speed regardless of headwind, up to a point where the headwind is well over half the TAS - it was counter-intuitive, as one felt that the headwind should require more airspeed.
Obviously the headwind diminishes range does but not so obviously does not seem to change the best speed to use, at least at lower wind speeds. It said to me that in a fuel critical situation, you power right back even with a headwind, unless the wind is very high (but I could not find an analytical method to determine at what relative headwind you must increase power)
Sorry this is a bit garbled but I think you get the drift. (must find that table..) Anybody got a better comment on this?
I once did the exercise of reading off best fuel consumption / speeds from the C172 POH curves and entered the figures against various headwinds into a table, to see how the range was affected by headwinds. (Can't find the spreadsheet....!) The result surprised me, with maximum range consistently being achieved with the still-air-most-economic-speed regardless of headwind, up to a point where the headwind is well over half the TAS - it was counter-intuitive, as one felt that the headwind should require more airspeed.
Obviously the headwind diminishes range does but not so obviously does not seem to change the best speed to use, at least at lower wind speeds. It said to me that in a fuel critical situation, you power right back even with a headwind, unless the wind is very high (but I could not find an analytical method to determine at what relative headwind you must increase power)
Sorry this is a bit garbled but I think you get the drift. (must find that table..) Anybody got a better comment on this?
