Vx for Propeller ac?
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Vx for Propeller ac?
Hi folks,
Trying to figure out why the best angle of climb speed for a prop. ac occurs at approx. 1.1 Vs and not Vimd. Best angle is down to max excess thrust and for a jet this will be at Vimd. Why not the same for a prop ac?
Bit confused???
Appreciate any help
Thanks
PM
Trying to figure out why the best angle of climb speed for a prop. ac occurs at approx. 1.1 Vs and not Vimd. Best angle is down to max excess thrust and for a jet this will be at Vimd. Why not the same for a prop ac?
Bit confused???
Appreciate any help
Thanks
PM
Gizajob
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[Recalls rusty ATPL knowledge]
The thrust curves for props and jets are different shapes (can't draw them here - sorry). That means that the maximum difference between those curves and the drag curve occurs at different points in the speed range.
The thrust curves for props and jets are different shapes (can't draw them here - sorry). That means that the maximum difference between those curves and the drag curve occurs at different points in the speed range.
Stand by for the real experts, but I find that 1.1 Vs to be a little lower than I would generally expect from common GA aircraft. Perhaps that is valid for higher powered aircraft. Reviewing my 1981 C-172RG manual, Vs at MTOW is 55.5 KCAS. (interpolated halfway between fwd and aft CG limits) SL Vx is published as 67 KIAS, (allthough 63 KIAS is the recommended obstacle clearance speed.) which when corrected to CAS is 68 KCAS. 68/55.5 = 1.225. The listed Vs assumes power off. The actual stall speed at full power is (by demonstration) somewhat lower than that due to prop thrust induced lift at the wing roots and the vertical component of thrust in a nose-high attitude. I would suspect that with a great deal more power available, the ratio of Vx/Vs would reduce signifigantly.
In fact, I saw Wayne Handley fly from a 90 degree nose up hover and accelerate straight up in his Turbo Raven at the Reno air races a few weeks before he crashed it at another airshow back in '99. A 90 degree angle of climb in a turboprop! A PT-6A in a very light airplane is a wonderous thing.
But back to the subject. The actual Vx for a particular prop aircraft would occur at the speed where the most excess thrust is available. So it will depend on the amount of thrust delivered and the low speed drag curve of the aircraft. In other words Vx will not be a fixed multiple of Vs. If one had to generalize across the GA fleet, I would guess that 1.2 to 1.3 Vs would usually be close. As always, when diving into performance problems, I stand ready to learn from a better (or more accurate!) answer. Fire away!
Best regards,
Westhawk
In fact, I saw Wayne Handley fly from a 90 degree nose up hover and accelerate straight up in his Turbo Raven at the Reno air races a few weeks before he crashed it at another airshow back in '99. A 90 degree angle of climb in a turboprop! A PT-6A in a very light airplane is a wonderous thing.
But back to the subject. The actual Vx for a particular prop aircraft would occur at the speed where the most excess thrust is available. So it will depend on the amount of thrust delivered and the low speed drag curve of the aircraft. In other words Vx will not be a fixed multiple of Vs. If one had to generalize across the GA fleet, I would guess that 1.2 to 1.3 Vs would usually be close. As always, when diving into performance problems, I stand ready to learn from a better (or more accurate!) answer. Fire away!
Best regards,
Westhawk
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Originally Posted by powdermonkey
Best angle is down to max excess thrust and for a jet this will be at Vimd
Differentials in thrust being small, it's the differentials in drag that creates the optimum, hence it is the speed for minimum drag.
Otherwise, the generic formula as stated by EGBKFLYER is always true:
Vx is the speed for maximum difference between thrust and drag (for a specific power settings since both curves vary with power settings).
Similarly, Vy is the speed for maximum difference between thrust power and drag power.
These 2 speeds are not directly related to Vs.
Luc
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Cheers guys, found a good and clear explanation in Oxford manual, so I get it now, thanks.
But can you clarify this?
In a glide, best angle is found when D/L is minimum....ie least drag for most lift which would be Vimd.
But for the best rate of descent again the notes say when D/L is minimum, but that min.D/L in this case is not Vimd but less than Vimd?
Also can anyone clarify what is going on in a descent with power for prop and jet ac?
......and does anyone fancy sitting my Perf. and PoF exams maybe???
But can you clarify this?
In a glide, best angle is found when D/L is minimum....ie least drag for most lift which would be Vimd.
But for the best rate of descent again the notes say when D/L is minimum, but that min.D/L in this case is not Vimd but less than Vimd?
Also can anyone clarify what is going on in a descent with power for prop and jet ac?
......and does anyone fancy sitting my Perf. and PoF exams maybe???
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The minimum rate of descent speed (or Vimp) is slightly lower than the minimum angle of descent speed (or Vimd) for the same physical reason that Vy is slightly higher than Vx.
In both cases, we compare a rate of altitude change per horizontal distance (in the air mass) with a rate of altitude change per time elapsed.
They relate to each other through the airspeed (and cosinus of the angle of descent which can be ignored on first approach).
dy/dx = v * dy/dt * cos(angle)
Now it is easily shown that a somewhat "simple" function that goes by 1 minimum or by 1 maximum, gets its minimum moved earlier on the curve
or its maximum moved later on the curve when the function is multiplied by the variable it acts upon.
I can send the math demonstration by MP, if you want.
So, if one names Yx(v) the function of angle of gliding descent per the airspeed, and Yt(v) the rate of gliding descent per the airspeed :
Yt(v) = v * Yxt(v)
(ignoring the cosinus of the angle)
and if Vimd is the minimum for Yx(v)
and Vimp is the minimum for Yt(v)
then Vimp < Vimd
Flying at Vimp, a lower speed than Vimd, one will fly longer although on a shorter distance
For Vx and Vy, we are looking for a maximum rate of climb,
Vx is the maximum for Yx(v)
and Vy is the maximum for Yt(v)
therefore Vy > Vx.
Flying at Vy, a higher speed than Vx, one will climb quicker although on a longer distance
Hope it clarifies the relationship between optimal angles of climb/descent and optimal rate of climb/descent.
Regards
Luc
In both cases, we compare a rate of altitude change per horizontal distance (in the air mass) with a rate of altitude change per time elapsed.
They relate to each other through the airspeed (and cosinus of the angle of descent which can be ignored on first approach).
dy/dx = v * dy/dt * cos(angle)
Now it is easily shown that a somewhat "simple" function that goes by 1 minimum or by 1 maximum, gets its minimum moved earlier on the curve
or its maximum moved later on the curve when the function is multiplied by the variable it acts upon.
I can send the math demonstration by MP, if you want.
So, if one names Yx(v) the function of angle of gliding descent per the airspeed, and Yt(v) the rate of gliding descent per the airspeed :
Yt(v) = v * Yxt(v)
(ignoring the cosinus of the angle)
and if Vimd is the minimum for Yx(v)
and Vimp is the minimum for Yt(v)
then Vimp < Vimd
Flying at Vimp, a lower speed than Vimd, one will fly longer although on a shorter distance
For Vx and Vy, we are looking for a maximum rate of climb,
Vx is the maximum for Yx(v)
and Vy is the maximum for Yt(v)
therefore Vy > Vx.
Flying at Vy, a higher speed than Vx, one will climb quicker although on a longer distance
Hope it clarifies the relationship between optimal angles of climb/descent and optimal rate of climb/descent.
Regards
Luc
Last edited by Luc Lion; 30th Mar 2006 at 15:35.
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Luc, I am very impressed. Thank you very much, and thank you all for responding...........only a few weeks to go and I shall be finished all 14!!!!!
What will I do with all that time off?
Cheers
PM
What will I do with all that time off?
Cheers
PM
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If you are studying for the JAR ATPL(A) exams then the things that you need to know are:
Vx is the speed at which maximum angle of climb is greatest.
The Sine of the climb angle = (Thrust-Drag) / Weight.
The Sine of an angle increases as the angle increases up to 1 at 90 degrees. So if we increase the Sine we will increase the climb angle. This means that for maximum climb angle we need maximum (Thrust-Drag) / Weight.
For any given weight the climb angle will be greatest when Thrust - Drag is greatest. Thrust-Drag is called excess thrust.
For jets, the thrust against TAS line is assumed (For POF purposes) to be horizontal, so the excess thrust is greatest at the speed at which drag is minimum. This speed is Vmd. So Vx jet is Vmd.
But for props the thrust line falls off rapidly with increasing airspeed. By the time we get to Vmd we have lost a significant part of the thrust. So the greatest excess thrust does not occur at Vmd. For the typical JAR ATPL(A) prop aircarft, excess thrust is slightly (perhaps a knot or two) less than Vmp. So Vx prop is slightly less than Vmp.
Vy is the speed at which the maximum rate of climb is greatest.
Rate of climb = (Power available - Power required) / Weight.
Power available - Power required is called Excess Power. So we get best rate of climb at the speed at excess power is greatest.
Power required is equal to drag x TAS. This means that as speed increases we are multilpying a bucket shaped drag curve by a straight line increase in TAS. This converts the bucket shaped drag curve into a power required curve that looks rather like a Nike Tick.
Power available = Thrust x TAS.
When TAS is zero, the power available = thrust x zero, so power available is zero when TAS is zero.
In jets, the constant thrust multilpied by a linear increase in TAS produces a straight line power available curve sloping up to the right as TAS increases. If we plot this on the same graph as the Nike Tick shaped power required curve we see that the greatest difference between the two (the excess power) occurs at a speed higher than Vmd. This is typically around 1.32 Vmd at low altitude. So Vy jet is greater than Vmd.
In props the thrust reduces as TAS increases. So when the downward curving thrust line is multiplied by a linear increase in TAS we get a power available curve that is bit like an inverted Nike Tick. This starts at zero when TAS is zero, increases with increasing TAS until it reaches a maximum value, then decreasing with further increases in TAS.
If we plot this on the same graph as the power required curve we will find that maximum excess power occurs at a speed slightly (a knot or two) higher than Vmp. So Vy prop is slightly higher than Vmp.
All of the above is of course just text book theory, so real-world aircraft will behave slightly differently.
We can find the speed for lowest sink rate (rate of descent) in a glide by looking at the energy situation.
When the engines are operating they give the aircraft energy. This is constantly being used up to do work in pushing the aircraft forward through the air. If the engines fail, then the aircraft can get no more energy, so it must use whatever energy it posesses at the time of the failure.
At any point in a flight an aircraft posesses kinetic energy (1/2mVsquared) by virtue of its velocity, and potential energy (Wh), by virtue of its height above the ground. When all of this energy has been used up the aircraft will have no velocity and no height, so it will be be standing still on the ground.
Glide endurance is the time that is taken to use up all of the energy posessed by the aircraft. The lower the rate of energy consumption, the longer will be the glide endurance. But the rate at which energy is consumed is power. So for minimum energy consumption rate and maximum glide endurance, we must fly at the speed at which power required is minimum. This speed is Vmp.
Glide endurance is also equal to height divided by sink rate. So when we have maximum glide endurance we also have minimum rate of descent. So Vmp can also be described as the speed for minimum sink rate.
Vx is the speed at which maximum angle of climb is greatest.
The Sine of the climb angle = (Thrust-Drag) / Weight.
The Sine of an angle increases as the angle increases up to 1 at 90 degrees. So if we increase the Sine we will increase the climb angle. This means that for maximum climb angle we need maximum (Thrust-Drag) / Weight.
For any given weight the climb angle will be greatest when Thrust - Drag is greatest. Thrust-Drag is called excess thrust.
For jets, the thrust against TAS line is assumed (For POF purposes) to be horizontal, so the excess thrust is greatest at the speed at which drag is minimum. This speed is Vmd. So Vx jet is Vmd.
But for props the thrust line falls off rapidly with increasing airspeed. By the time we get to Vmd we have lost a significant part of the thrust. So the greatest excess thrust does not occur at Vmd. For the typical JAR ATPL(A) prop aircarft, excess thrust is slightly (perhaps a knot or two) less than Vmp. So Vx prop is slightly less than Vmp.
Vy is the speed at which the maximum rate of climb is greatest.
Rate of climb = (Power available - Power required) / Weight.
Power available - Power required is called Excess Power. So we get best rate of climb at the speed at excess power is greatest.
Power required is equal to drag x TAS. This means that as speed increases we are multilpying a bucket shaped drag curve by a straight line increase in TAS. This converts the bucket shaped drag curve into a power required curve that looks rather like a Nike Tick.
Power available = Thrust x TAS.
When TAS is zero, the power available = thrust x zero, so power available is zero when TAS is zero.
In jets, the constant thrust multilpied by a linear increase in TAS produces a straight line power available curve sloping up to the right as TAS increases. If we plot this on the same graph as the Nike Tick shaped power required curve we see that the greatest difference between the two (the excess power) occurs at a speed higher than Vmd. This is typically around 1.32 Vmd at low altitude. So Vy jet is greater than Vmd.
In props the thrust reduces as TAS increases. So when the downward curving thrust line is multiplied by a linear increase in TAS we get a power available curve that is bit like an inverted Nike Tick. This starts at zero when TAS is zero, increases with increasing TAS until it reaches a maximum value, then decreasing with further increases in TAS.
If we plot this on the same graph as the power required curve we will find that maximum excess power occurs at a speed slightly (a knot or two) higher than Vmp. So Vy prop is slightly higher than Vmp.
All of the above is of course just text book theory, so real-world aircraft will behave slightly differently.
We can find the speed for lowest sink rate (rate of descent) in a glide by looking at the energy situation.
When the engines are operating they give the aircraft energy. This is constantly being used up to do work in pushing the aircraft forward through the air. If the engines fail, then the aircraft can get no more energy, so it must use whatever energy it posesses at the time of the failure.
At any point in a flight an aircraft posesses kinetic energy (1/2mVsquared) by virtue of its velocity, and potential energy (Wh), by virtue of its height above the ground. When all of this energy has been used up the aircraft will have no velocity and no height, so it will be be standing still on the ground.
Glide endurance is the time that is taken to use up all of the energy posessed by the aircraft. The lower the rate of energy consumption, the longer will be the glide endurance. But the rate at which energy is consumed is power. So for minimum energy consumption rate and maximum glide endurance, we must fly at the speed at which power required is minimum. This speed is Vmp.
Glide endurance is also equal to height divided by sink rate. So when we have maximum glide endurance we also have minimum rate of descent. So Vmp can also be described as the speed for minimum sink rate.
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Also impressive, and correct
(but for "So Vx prop is slightly less than Vmp" that should read "So Vx prop is slightly less than Vmd"
So, PowderMonkey, with Keith's explanations on combining thrust curve and drag curve you know why Vx <= Vmd (with Vx = Vmd for jets),
and with his explanations on combining power available curve and power required curve, you have why Vmp < Vy.
And with my post you have why Vx < Vy and why Vmp < Vmd
Eventually you have
Vmp < Vx <= Vmd < Vy
The fact that Vmd is lower than Vy is obvious when Vx = Vmd (engine with almost constant thrust).
It stays in that relation as long as the effect of drag increase at speed lower than Vmd
is more important than the effect of engine thrust decrease as speed get higher than Vmp.
Luc
(but for "So Vx prop is slightly less than Vmp" that should read "So Vx prop is slightly less than Vmd"
So, PowderMonkey, with Keith's explanations on combining thrust curve and drag curve you know why Vx <= Vmd (with Vx = Vmd for jets),
and with his explanations on combining power available curve and power required curve, you have why Vmp < Vy.
And with my post you have why Vx < Vy and why Vmp < Vmd
Eventually you have
Vmp < Vx <= Vmd < Vy
The fact that Vmd is lower than Vy is obvious when Vx = Vmd (engine with almost constant thrust).
It stays in that relation as long as the effect of drag increase at speed lower than Vmd
is more important than the effect of engine thrust decrease as speed get higher than Vmp.
Luc
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Thank you for all those great replies, I'm feeling at tad silly now, I guess I'm just a little burned out coming towards the end of these exams......just too much info over the last year, none of it seems to make any sense now. Maybe I should do them again, make sure I've really understood everything..........NOT BLOODY LIKELY!!!!!
I hope you guys are ATPL instructors though, I would hate to think you guys are ordinary joes like me who actually "get it"....I'm just treading water in a sea of facts and figures here!
Cheers
PM
I hope you guys are ATPL instructors though, I would hate to think you guys are ordinary joes like me who actually "get it"....I'm just treading water in a sea of facts and figures here!
Cheers
PM
