Variation of VR/V2 with temperature?

[Spanglish]

Hi all,

I am going through some passed papers for a performance exam and would like some help understanding the reasoning behind the following question.

For the same pressure altitude how does VR/V2 change with an increase in temperature?

I have looked everywhere and discussed it with various collegues and we can't seem to agree on an answer.

Thanks in advance.

[nick14]

I would imagine there would be an increase in the speeds with an increase in temperature.

Rise in temperature gives drop in pressure and density. Vr is based on Vmu, Vmu is to do with lift generated by the wings at max AOA on the ground so I would think it will increase with an increase in temp.

Just my simple understanding.

[de facto]

TAS icreases with increase in temperature.
So for a given VR, your speed across the Air mass will be higher.
Reason why perf using assumed higher temperature is a conservative method in the STOP (v1) and the GO (V2) decision.

[HazelNuts39]

The speed increment between Vr and V2 in terms of TAS is proportional to thrust minus drag. Below the flat-rated temperature thrust is constant and V2-Vr is approximately constant in terms of TAS, but reduces with increasing temperature in terms of IAS.

Above the flat-rated temperature thrust reduces with temperature and hence acceleration. V2-Vr then reduces with increasing temperature in terms of TAS as well as in IAS.

[de facto]

The speed increment between Vr and V2 in terms of TAS is proportional to thrust minus drag. Below the flat-rated temperature thrust is constant and V2-Vr is approximately constant in terms of TAS, but reduces with increasing temperature in terms of IAS.

Above the flat-rated temperature thrust reduces with temperature and hence acceleration. V2-Vr then reduces with increasing temperature in terms of TAS as well as in IAS.


Spanglish, I think you got a detailed info alright:E

[MD83FO]

In our takeoff performance software LPC, all the speeds remain the same all the way to the flex temp.

[HazelNuts39]

MD83FO;

When using 'flexible' thrust settings (except when limited by Vmc which is determined for the actual temperature), speeds and distances are determined at the assumed temperature, which is conservative for lower temperatures.

[Natstrackalpha]

your increase in temp is going to reduce air density, so effectively your density alt. If we look at a massive temp increase. Then an airfield with an elev of 2,000` and an outside temp of 40 deg C, is going to perform as if it was at a much higher altitutde. get it?
Less dense. More forwards speed required (G/S) to achieve the same airspeed (TAS)
therefore need a longer runway. Have you got a longer runway? If not, either you don`t go, or you unload cargo, why would you do that? Or aska few passengers to disembark ( hint,start with the cargo first . . ) you may consider removing some fuel, not an option that most, if not all pilots tend to entertain, although physically possible, you will then have to change you flight routing and alternates etc. etc., etc. - figure out your speed adjustment from all that and it should come easy now. ok? Good luck with it all.

[hawk37]

Spanglish asks "For the same pressure altitude how does VR/V2 change with an increase in temperature?"

If you mean for a particular take off weight, then for any jet I've flown, Vr and V2 remain the same, regardless of any change in temperature.

[Old Smokey]

Are we overlooking the obvious here?

As temperature increases, the Limiting Takeoff Weight (or Regulated Takeoff Weight) reduces. That's normal for pretty much every aircraft flying. Reduced weights require reduced speeds. Thus, V1, Vr, and V2 will all reduce.

I rest my case your honour.

Best Regards,

Old Smokey

[Occy]

Spanglish asks "For the same pressure altitude how does VR/V2 change with an increase in temperature?"

If you mean for a particular take off weight, then for any jet I've flown, Vr and V2 remain the same, regardless of any change in temperature. El correcto

[hawk37]

Smokey,

the OP made no mention of limiting the take off weight, just to keep the PA the same and vary the temperature. He made no reference to the situation of maximum allowed take off weight.

[Icelanta]

Guys, Keep it simple and correct:

1) V1 is Thrust related so depends on your density and temperature (thus also your flex. tmp. calculations)

2) Vr and V2 are always MASS related and are the same for a certain Take-off Mass. They do not change unless your payload or fuel changes.

3) Your MTOM depends Runway length and condition (think contamination or up/downslope), ambient temperature and density.

[Airmann]

It's actually an interesting question, if you take a look at airbus' published INDICATED Vr and V2 speeds they decrease as temp increases but you're being fooled:

E.g.
This is directly out of the airbus A320 T/O quick reference charts:

As an example for a Config 1+F T/O from a 3000m runway @ PA:0ft:

@-20 degrees: Vr: 162KIAS (KTAS:152) V2:164KIAS (KTAS:154)

@ 50 degrees: Vr: 150KIAS (KTAS:159) V2: 152KIAS (KTAS:161)

So the Vr and V2 INDICATED speeds (the ones published on the chart) DECREASE as temperature increases but when you convert them to TAS you'll find the opposite: the TRUE speed INCREASE as temp increase.

Don't let the indicated temperatures fool you, the aircraft needs a higher TAS through the air to fly in warmer air.

[hawk37]

Airmann,

Are these different Vr and V2 speeds for the same take off weight?

[Airmann]

No the max t/o weights are obviously different. But nevertheless, the higher TAS are for a lower max T/O weight. One would have to look at TAS over IAS. If anything IAS means nothing in terms of aerodynamics, it's just what the pilot is looking at, and gives him a reference by which to fly the aircraft.

[hawk37]

Airmann,

If the take off weight changes, then of course V2 changes.

However, for the same weights, do V2 and Vr change as pressure altitude and/or temperature changes? You have the data?

Does MD83FO have it right, way back in post 6?

[Airmann]

No hawk, it's a little difficult to do a comparison of weights because of the way airbus have set up their charts. When we calculate t/o speeds and flex temp for given conditions, we always use the speeds computed for a given runway length, pressure alt and temp, regardless of our weight because we assume the highest permissible RTOW and use those speeds, the speeds would never change, only the flex temp would. Yes MD83FO has it right.

For example with the numbers I have used above at -20 degrees the max RTOW is 83.8. And the calculated V speeds are based off the assumption of a 3000 meter runway, -20 degrees and 0ft PA and 83.8t. Now suppose the aircraft was only loaded to 70t TOW. We would find that the max ambient temp at which a 70t a/c could takeoff given the runway length and PA. In this case it would be ~67 degrees. So we would use a flex of 67 but the V speeds would not change. If on the other hand we had a a/c loaded to 77t the max temp given the runway and PA is ~51. So we would use flex 51 BUT THE SAME SPEEDS AS BEFORE.

Now I understand this is a quirk of Airbus as they base their speeds off the max RTOW, so all aircraft using those numbers are safe, If its any help the max RTOW in the first instance (-20 degrees) is 83.8t, whereas the max RTOW in the second instance is 77.6t (50 degrees). So even with a LOWER TOW (77.6t) the V speeds when expressed in TAS are higher due to the lower temp. The temperature is dictating the speeds in this instance not the weights.


BTW this is not to say weight doesn't have an effect, it's just that airbus don't let it by always assuming the max permissible T/O weight. I think that if someone had charts from something smaller, a piper or Cessna we could find the answer.

[Spanglish]

This question comes up in 2 different past papers for the HK CAD performance exam and the supposed right answer is..

VR increases, V2 decreases.

Thanks for your input folks.

Spanglish

[keith williams]

It is possible that the HK Authorities are using JAR/EASA based material.

If you go to the UK CAA website and search for CAP 698 you will find the performance manual that is used for the JAR/EASA performance exams. This book is based on an early version BOEING 737 with engine flat rated to ISA +15 degrees Celsius.

If you open the PDF and go into pages 65, 66 and 67 you will find tables for the V1, VR and V2. These tables are based on balanced take-offs, with no stopway or clearway.

On page 65 you will see a table that allocates letters A, B, C, D, E or F for increases in temperature or pressure altitude.

On pages 66 and 67 you will find tables for various conbinations of temperature/PA, weights and flap settings.

If you select one of these tables and pick a fixed weight, then move from left to right across the you will see how V1, VR and V2 vary with increasing temperature or pressure altitude for this aircraft undertaking this type of take-off.

In many cases there is no change until you get to the high temperatures.

[hawk37]

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?

[HazelNuts39]

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).

[keith williams]

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.



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.

[hawk37]

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!!

[HazelNuts39]

It would be interesting to have the V stall speedsJust an educated guess:
http://i.imgur.com/NFxOs.gif

http://i.imgur.com/lIdBc.gif?1 (http://imgur.com/lIdBc)

[HazelNuts39]

For this type of aircraft V2 must be at least 1.13 Vsr and 1.1 Vmca.Agreed, but Vmca changes very little with weight. Therefore I think that V2>1.2Vs is due to Vmu limiting Vr for this airplane.

[keith williams]

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?

[HazelNuts39]

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.

[keith williams]

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?

[HazelNuts39]

the figures show V1 and VR decreasing with increasing temperature, while V2 does the opposite. Please give an example.

[keith williams]

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.

[HazelNuts39]

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.

http://i.imgur.com/3DeGP.gif

[orninn]

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.

:8

[HazelNuts39]

For some reason an actual Boeing take off speed table tells a different story...
Not really. The story it tells is that this speed schedule is governed by Vmu - see earlier in this thread.
That is, if we would rotate at a speed equal to 1,05Vmc we would reach Vlof at a speed lower than 1,1Vmu.That is not correct. Vmc and Vmu are independent variables. You're assuming a relation between them that does not exist.
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.Except that V2 is also related to Vr. Any criterion that pushes Vr up, pushes V2 with it to a value higher than the minima you quote here.