Variation of VR/V2 with temperature?
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Keith,
I did download the performance manual. Does it seem strange to you that V2 is lower at higher pressure altitudes, up to 4 knots for the same weight?
Any additive for compressibility, although a small factor at this low a speed, would surely increase V2 at higher pressure altitudes.
From what I've seen, V2 has nearly always been exactly 1.2 V stall, simply because manufacturers want the best runway performance, and while V2 can be higher than 1.2 V stall, this would increase runway requirement.
I understand improved climb. However looking at the reference you provided, I see no indication that the example is for that case.
I'm half wondering if position error corrections for the airspeed indicator can provide an explanation, although the only corrections I've seen for jets at this low a speed were a fixed amount, up 2 knot IAS, and regardless of the pressure altitude. It was only once airspeed became greater than 160 knots that position error had pressure altitude corrections applied (as well as the correction depending on airspeed , of course), and temperature was not a factor.
Anyone?
I did download the performance manual. Does it seem strange to you that V2 is lower at higher pressure altitudes, up to 4 knots for the same weight?
Any additive for compressibility, although a small factor at this low a speed, would surely increase V2 at higher pressure altitudes.
From what I've seen, V2 has nearly always been exactly 1.2 V stall, simply because manufacturers want the best runway performance, and while V2 can be higher than 1.2 V stall, this would increase runway requirement.
I understand improved climb. However looking at the reference you provided, I see no indication that the example is for that case.
I'm half wondering if position error corrections for the airspeed indicator can provide an explanation, although the only corrections I've seen for jets at this low a speed were a fixed amount, up 2 knot IAS, and regardless of the pressure altitude. It was only once airspeed became greater than 160 knots that position error had pressure altitude corrections applied (as well as the correction depending on airspeed , of course), and temperature was not a factor.
Anyone?
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hawk37;
Vstall is one of the five constraints which limit the takeoff speed schedule. The others are: Vmca, Vmcg, Vmu (engine out) and Vmu (all engines). Any of the other four may force V2 to be greater than 1.2 Vs (1.13 Vsr in current regulation).
Vstall is one of the five constraints which limit the takeoff speed schedule. The others are: Vmca, Vmcg, Vmu (engine out) and Vmu (all engines). Any of the other four may force V2 to be greater than 1.2 Vs (1.13 Vsr in current regulation).
I did download the performance manual. Does it seem strange to you that V2 is lower at higher pressure altitudes, up to 4 knots for the same weight?
It does seem strange, but the author took the figures from the performance manual for a real aircraft, so I have to assume that they are correct.
Any additive for compressibility, although a small factor at this low a speed, would surely increase V2 at higher pressure altitudes.
From what I've seen, V2 has nearly always been exactly 1.2 V stall, simply because manufacturers want the best runway performance, and while V2 can be higher than 1.2 V stall, this would increase runway requirement.
I understand improved climb. However looking at the reference you provided, I see no indication that the example is for that case.
From what I've seen, V2 has nearly always been exactly 1.2 V stall, simply because manufacturers want the best runway performance, and while V2 can be higher than 1.2 V stall, this would increase runway requirement.
I understand improved climb. However looking at the reference you provided, I see no indication that the example is for that case.
The figures in the V Speed tables are not specifically for the improved climb take-off technique. This subject is dealt with later in the book.
I'm half wondering if position error corrections for the airspeed indicator can provide an explanation, although the only corrections I've seen for jets at this low a speed were a fixed amount, up 2 knot IAS, and regardless of the pressure altitude. It was only once airspeed became greater than 160 knots that position error had pressure altitude corrections applied (as well as the correction depending on airspeed , of course), and temperature was not a factor.
I have never found a definitive explanation of why the figures behave the way they do. My hypothesis goes something like this:
Increasing pressure altitude or temperature tend to:
1.Reduce thrust, which reduces acceleration rate.
2.Increase the TAS : CAS ratio, which increases the acceleration required during take-off.
The engines on this aircraft are flat rated to ISA+15 at MSL, so until this limit is reached, only the increasing TAS:CAS ratio affects the take-off.
The acceleration problem is most critical between observing the engine failure at V1 and reaching V2. So to reduce this problem V1 should be increased and V2 should be decreased. Any significant increase in V1 will require an increase in VR.
For this type of aircraft V2 must be at least 1.13 Vsr and 1.1 Vmca. At the low end of the temperature / altitude scale the constant flat rated thrust will maintain constant Vmca, so the potential to reduce V2 will be restricted. But at higher temperatures and altitudes the reducing thrust will reduce Vmca, making it possible to reduce V2 until it becomes limited by 1.13 Vsr,
This gives an overall sequence of:
1.No changes to V1, VR or V2 while temperatures and altitude are
low.
2.Increasing V1 and Vr after the flat rate limit has been exceeded.
3.Decreasing V2 at higher temperatures and altitudes when the reduced Vmca permits.
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Keith,
Just to confirm, your hypothesis then is that V2 at the lowest weight of 40,000 kg and when in area A (low PA, low temperature) may be greater than 1.2 Vs?
If so then I understand what you have written. It would be interesting to have the V stall speeds that were used for certification, so that one can multiply them by 1.2 and compare this number to the published V2.
good explanations!!
Just to confirm, your hypothesis then is that V2 at the lowest weight of 40,000 kg and when in area A (low PA, low temperature) may be greater than 1.2 Vs?
If so then I understand what you have written. It would be interesting to have the V stall speeds that were used for certification, so that one can multiply them by 1.2 and compare this number to the published V2.
good explanations!!
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Originally Posted by keith W
For this type of aircraft V2 must be at least 1.13 Vsr and 1.1 Vmca.
Looking at the values of V2 against weight for any given combination of temperature and altitude, I can see that there is a square root relationship. This might indicate that V2 is being determined by the stall speed. But presumably Vmu is also related to the square root of weight, so this might be the limiting factor.
If we take any given low weight and move left to right, the increasing temperature and altitude cause V2 to gradually reduce. But if we choose a high weight V2 initially remains constant then gradually reduces. Would this be the case if Vmu were the limiting factor?
If we take any given low weight and move left to right, the increasing temperature and altitude cause V2 to gradually reduce. But if we choose a high weight V2 initially remains constant then gradually reduces. Would this be the case if Vmu were the limiting factor?
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keith,
The speed values in the table are rounded to the nearest knot, so they are only accurate to within +/- 0.5 kt at best. At high weight (close to WAT-limit hence minimum thrust/weight) V2 is 1.2 Vs for both flap settings and conditions A through F.
I find it difficult to make a general statement on Vmu. If it is only limited by the maximum body angle it is a function of thrust/weight due to the vertical component of thrust. However, very often elevator power (i.e. the minimum speed at which the nosewheel can be lifted off the runway) enters into the determination of Vmu, in particular the all-engines Vmu. The relations between Vmu, Vr and V2 are functions of thrust/weight, so it's getting rather complex.
The speed values in the table are rounded to the nearest knot, so they are only accurate to within +/- 0.5 kt at best. At high weight (close to WAT-limit hence minimum thrust/weight) V2 is 1.2 Vs for both flap settings and conditions A through F.
I find it difficult to make a general statement on Vmu. If it is only limited by the maximum body angle it is a function of thrust/weight due to the vertical component of thrust. However, very often elevator power (i.e. the minimum speed at which the nosewheel can be lifted off the runway) enters into the determination of Vmu, in particular the all-engines Vmu. The relations between Vmu, Vr and V2 are functions of thrust/weight, so it's getting rather complex.
Last edited by HazelNuts39; 8th Jun 2012 at 11:20. Reason: AEO Vmu
When teaching this subject in the past I found that all students were puzzled by the fact that the figures show V1 and VR decreasing with increasing temperature, while V2 does the opposite.
As I said in an earlier post, I have never seen a definitive explanation of this curiosity, but had surmised that it was due to the decreasing value of 1.1 Vmca. Having looked more closely at the figures I can see that this is not the case.
Can you suggest a (not too complex) explanation?
As I said in an earlier post, I have never seen a definitive explanation of this curiosity, but had surmised that it was due to the decreasing value of 1.1 Vmca. Having looked more closely at the figures I can see that this is not the case.
Can you suggest a (not too complex) explanation?
Going through the letters A to F represents increasing temperature and/or increasing altitude.
If we take 45000 Kg with flap 5 we have the following figures
A V1 121 VR 123 V2 136
B V1 122 VR 124 V2 135
C V1 122 VR 125 V2 135
D V1 124 VR 126 V2 135
E V1 125 VR 127 V2 134
F V1 128 VR 128 V2 134
Although there are some flat areas, the general trend is V1 and VR increasing while V2 decreases.
If we take 45000 Kg with flap 5 we have the following figures
A V1 121 VR 123 V2 136
B V1 122 VR 124 V2 135
C V1 122 VR 125 V2 135
D V1 124 VR 126 V2 135
E V1 125 VR 127 V2 134
F V1 128 VR 128 V2 134
Although there are some flat areas, the general trend is V1 and VR increasing while V2 decreases.
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The speed increment between Vr and V2 incurred during rotation and transition to steady climb increases with increasing thrust-to-weight ratio, i.e. with reducing temperature:
A V1 121 VR 123 V2 136 V2-Vr 13
B V1 122 VR 124 V2 135 V2-Vr 11
C V1 122 VR 125 V2 135 V2-Vr 10
D V1 124 VR 126 V2 135 V2-Vr 9
E V1 125 VR 127 V2 134 V2-Vr 7
F V1 128 VR 128 V2 134 V2-Vr 6
V1 is selected to 'balance' the accelerate-stop distance and the take-off distance. That is a different subject from the original post that I don't really want to get into.
PS
See also my post #4 for TAS/CAS.
A V1 121 VR 123 V2 136 V2-Vr 13
B V1 122 VR 124 V2 135 V2-Vr 11
C V1 122 VR 125 V2 135 V2-Vr 10
D V1 124 VR 126 V2 135 V2-Vr 9
E V1 125 VR 127 V2 134 V2-Vr 7
F V1 128 VR 128 V2 134 V2-Vr 6
V1 is selected to 'balance' the accelerate-stop distance and the take-off distance. That is a different subject from the original post that I don't really want to get into.
PS
See also my post #4 for TAS/CAS.
Last edited by HazelNuts39; 9th Jun 2012 at 12:49. Reason: typo, PS, graph
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Vr and V2
Here is how I see this, theoretically speaking. For some reason an actual Boeing take off speed table tells a different story...
According do Oxford aviation academy performance book, chapter 14 pages 375 and 376
Regarding Vr:
May not be less than:
V1
1,05 VMC
Speed such that V2 may be attained before 35ft
A speed that, if the aeroplane is rotated at its maximum practical rate, will result in VLOF of not less than 1,1VMU (1,05VMU one eng. inop case)
At a low density altitude (high density) the 1,05Vmc requirement will be limiting for Vr, i.e. the rotation speed is governed by the requirement that we can not start the rotation at a speed lower than 1,05Vmc .
As density altitude increases (lower density) the Vmc is reduced as well, causing the Vr to reduce with it.
Eventually the Vr becomes limited by the maximum practical rotation rate due to the 1,1 Vmu requirement. That is, if we would rotate at a speed equal to 1,05Vmc we would reach Vlof at a speed lower than 1,1Vmu. So from a certain density altitude, going up, the Vr will increase.
As for the V2 speed:
V2min in terms of CAS may not be less than
1,13 VSR
1,1 Vmc
At a low density altitude the V2 will initially be limited by the 1,1Vmc requirement. As the density altitude gets higher, the Vmc is reduced and so is the V2 with it until reaching the 1,13Vsr limit where the V2 becomes a fixed number.
According do Oxford aviation academy performance book, chapter 14 pages 375 and 376
Regarding Vr:
May not be less than:
V1
1,05 VMC
Speed such that V2 may be attained before 35ft
A speed that, if the aeroplane is rotated at its maximum practical rate, will result in VLOF of not less than 1,1VMU (1,05VMU one eng. inop case)
At a low density altitude (high density) the 1,05Vmc requirement will be limiting for Vr, i.e. the rotation speed is governed by the requirement that we can not start the rotation at a speed lower than 1,05Vmc .
As density altitude increases (lower density) the Vmc is reduced as well, causing the Vr to reduce with it.
Eventually the Vr becomes limited by the maximum practical rotation rate due to the 1,1 Vmu requirement. That is, if we would rotate at a speed equal to 1,05Vmc we would reach Vlof at a speed lower than 1,1Vmu. So from a certain density altitude, going up, the Vr will increase.
As for the V2 speed:
V2min in terms of CAS may not be less than
1,13 VSR
1,1 Vmc
At a low density altitude the V2 will initially be limited by the 1,1Vmc requirement. As the density altitude gets higher, the Vmc is reduced and so is the V2 with it until reaching the 1,13Vsr limit where the V2 becomes a fixed number.
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Originally Posted by orninn
For some reason an actual Boeing take off speed table tells a different story...
That is, if we would rotate at a speed equal to 1,05Vmc we would reach Vlof at a speed lower than 1,1Vmu.
As the density altitude gets higher, the Vmc is reduced and so is the V2 with it until reaching the 1,13Vsr limit where the V2 becomes a fixed number.
Last edited by HazelNuts39; 4th Nov 2012 at 11:13.
