Vr and Pressure Altitude

[Dick Whittingham]

The following has been given to me to solve, but as a bear of very smal brain, may I ask the experts of this forum to help, please?

737 at 40tonnes at SL, book gives Vr as 114KIAS. At PA 8000 to 10000ft the book gives 120KIAS. Excepting EAS/IAS errors, that should not be significant at these speeds and heights, why does Vr go up at all, and how does it make such a large jump, 6kt?

Anything to do with rate of acceleration through to Vlo or V2?

Dick Whittingham

[Pugilistic Animus]

I'm guessing to meet required climb gradients. put a little 'zoom' into it and get things back to evens as maybe.

[Mad (Flt) Scientist]

I'd guess it's the Vr-V2 speed spread, especially if you have a constant (or near-enough) V2 at the same altitudes.

Since it's really a thrust issue, if there's a specific FADEC schedule with a steep gradient of thrust with altitude, that might explain the Vr-V2 (and hence the Vr also) having a discontinuous behaviour.

If on the other hand it's a case of the V2 ALSO varying similarly, I don't think it would be for climb gradient reasons; more likely would be that the increased Mach number for the same IAS at higher alts is causing a small but significant change to stall speeds, and hence to any speed scheduled on minimum speed ratios.

[Miles Magister]

It is the same reason that all your speeds change with an increase in altitude. Density, mass flow etc. You just need more speed to achieve the same mass flow and get sufficient bernoulis across your wing.

You need to find a set of APTL notes on performance from a while ago which include the D&X calculations from first priciples. Sorry don't have any to hand but some descent chap who flew in the days of comets etc might be able to help you.

[Dick Whittingham]

"..some decent chap who flew in the days of Comets etc.."
That'll be me then.
Dick W

P.S. Thanks, MFS

[Alex Whittingham]

Thanks MFS. We're discussing this in the office Looking at the regs I have two areas where thrust might be relevant, 25.107(e)(1)(iii) or 25.107(e)(3). The first is the VR V2 speed spread but could para 3 be an issue on the 737?

I'm sure you know the JARs, to save you looking them up:

JAR 25.107(e) VR, in terms of calibrated air speed, must be selected in accordance with the conditions of subparagraphs (1) to (4) of this paragraph:

(1) VR may not be less than –
(i) V1;
(ii) 105% of VMC;
(iii) The speed (determined in accordance with JAR 25.111(c)(2)) that allows reaching V2 before reaching a height of 35 ft above the take-off surface; or
(iv) A speed that, if the aeroplane is rotated at its maximum practicable rate, will result in a VLOF of not less than –
[(A) 110% of VMU in the all-engines-operating condition and] 105% of VMU determined at the thrust-to-weight ratio corresponding to the one-engine-inoperative condition; or
[(B) If the VMU attitude is limited by the geometry of the aeroplane (i.e., tail contact with the runway), 108% of VMU in the all-engines-operating condition and 104% of VMU determined at the thrust-to-weight ratio corresponding to the one-engine-inoperative condition. (See ACJ 25.107(e)(1)(iv).) ]

(2) For any given set of conditions (such as weight, configuration, and temperature), a single value of VR, obtained in accordance with this paragraph, must be used to show compliance with both the one-engine-inoperative and the all-engines-operating take-off provisions.

(3) It must be shown that the one-engine-inoperative take-off distance, using a rotation speed of 5 knots less than VR established in accordance with sub-paragraphs (e)(1) and (2) of this paragraph, does not exceed the corresponding one-engine-inoperative take-off distance using the
established VR. The take-off distances must be determined in accordance with JAR 25.113(a)(1). (See ACJ 25.107(e)(3).)

[Mad (Flt) Scientist]

It ought to be possible to determine which of 25.107(e)(1)(iii) or 25.107(e)(3) is determining Vr by looking at V2.

If the V2 is constant, then I'd be pretty much certain that speed spread is driving Vr, since a constant V2 would imply that one of the V2 requirements is dominating, and that Vr is being determined based on V2, which would point the finger at (e)(1)(iii).

If the V2 is non-constant, then I'd be a bit more suspicious that it might be something else, but I'd still be more inclined to look for one of the V2-drivers, not (e)(3). The Vr-5 requirement is also an OEI case, so the thrust/weight isn't varying between the Vr and Vr-5 cases for (e)(3) at a specific altitude; I'd therefore expect that if the Vr-5 case is driving the choice of Vr that it would be doing so independent of thrust (and hence altitude).

I'd have thought the Vrmin requirement (e)(1)(iv) would be more likely to drive Vr than trying to balance the Vr and Vr-5 cases, though. For the Vr-5 case to be important you'd have to be rotating at a pretty low speed, so that either:
(1)the increased alpha at lift-off is pushing up the drag relative to the Vr case and seriously degrading the in-air portion of the takeoff (since the ground run is about 10% short to start with, the in-air portion has to take quite a hit); or
(2) you aren't actually achieving Vlof any earlier, and the aircraft ends up doing something close to the cert Vmu test - but that would only be the case is Vr is really close to Vmu, hence my comment about (e)(1)(iv)