V-speed derivations - help please!!

[Captain Phaedrus]

Esteemed colleagues,

I'm having trouble finding a web resource for the definitive derivations of V2, Vref etc. Yes, I've searched here, but without finding what I'm after.

I need notes which give full chaper and verse (JAR if it makes a difference) on the relationships between V2 and Vref and Vs etc.

Over to you - oh, and by tomorrow morning would be great <big grin>.

[747FOCAL]

hmmm let see........


25.103 Stall speed.

(a) The reference stall speed, VSR, is a calibrated airspeed defined by the applicant. VSR may not be less than a 1-g stall speed. VSR is expressed as:



where:

VCLMAX = Calibrated airspeed obtained when the load factor-corrected lift coefficient




is first a maximum during the maneuver prescribed in paragraph (c) of this section. In addition, when the maneuver is limited by a device that abruptly pushes the nose down at a selected angle of attack (e.g., a stick pusher), VCLMAX may not be less than the speed existing at the instant the device operates;

nZW = Load factor normal to the flight path at VCLMAX

W = Airplane gross weight;

S = Aerodynamic reference wing area; and

q = Dynamic pressure.

(b) VCLMAX is determined with:

(1) Engines idling, or, if that resultant thrust causes an appreciable decrease in stall speed, not more than zero thrust at the stall speed;

(2) Propeller pitch controls (if applicable) in the takeoff position;

(3) The airplane in other respects (such as flaps and landing gear) in the condition existing in the test or performance standard in which VSR is being used;

(4) The weight used when VSR is being used as a factor to determine compliance with a required performance standard;

(5) The center of gravity position that results in the highest value of reference stall speed; and

(6) The airplane trimmed for straight flight at a speed selected by the applicant, but not less than 1.13VSR and not greater than 1.3VSR.

(c) Starting from the stabilized trim condition, apply the longitudinal control to decelerate the airplane so that the speed reduction does not exceed one knot per second.

(d) In addition to the requirements of paragraph (a) of this section, when a device that abruptly pushes the nose down at a selected angle of attack (e.g., a stick pusher) is installed, the reference stall speed, VSR, may not be less than 2 knots or 2 percent, whichever is greater, above the speed at which the device operates.

[Doc. No. 28404, 67 FR 70825, Nov. 26, 2002]

25.105 Takeoff.

(a) The takeoff speeds described in § 25.107, the accelerate-stop distance described in § 25.109, the takeoff path described in § 25.111, and the takeoff distance and takeoff run described in § 25.113, must be determined --

(1) At each weight, altitude, and ambient temperature within the operational limits selected by the applicant; and

(2) In the selected configuration for takeoff.

(b) No takeoff made to determine the data required by this section may require exceptional piloting skill or alertness.

(c) The takeoff data must be based on --

(1) In the case of land planes and amphibians:

(i) Smooth, dry and wet, hard-surfaced runways; and

(ii) At the option of the applicant, grooved or porous friction course wet, hard-surfaced runways.

(2) Smooth water, in the case of seaplanes and amphibians; and

(3) Smooth, dry snow, in the case of skiplanes.

(d) The takeoff data must include, within the established operational limits of the airplane, the following operational correction factors:

(1) Not more than 50 percent of nominal wind components along the takeoff path opposite to the direction of takeoff, and not less than 150 percent of nominal wind components along the takeoff path in the direction of takeoff.

(2) Effective runway gradients.

[Doc. No. 5066, 29 FR 18291, Dec. 24, 1964, as amended by Amdt. 25-92, 63 FR 8318, Feb. 18, 1998]


§ 25.107 Takeoff speeds.

(a) V1 must be established in relation to VEF as follows:

(1) VEF is the calibrated airspeed at which the critical engine is assumed to fail. VEF must be selected by the applicant, but may not be less than VMCG determined under § 25.149(e).

(2) V1, in terms of calibrated airspeed, is selected by the applicant; however, V1 may not be less than VEF plus the speed gained with critical engine inoperative during the time interval between the instant at which the critical engine is failed, and the instant at which the pilot recognizes and reacts to the engine failure, as indicated by the pilot's initiation of the first action (e.g., applying brakes, reducing thrust, deploying speed brakes) to stop the airplane during accelerate-stop tests.

(b) V2MIN, in terms of calibrated airspeed, may not be less than --

(1) 1.13 VSR for --

(i) Two-engine and three-engine turbopropeller and reciprocating engine powered airplanes; and

(ii) Turbojet powered airplanes without provisions for obtaining a significant reduction in the one-engine-inoperative power-on stall speed;

(2) 1.08 VSR for --

(i) Turbopropeller and reciprocating engine powered airplanes with more than three engines; and

(ii) Turbojet powered airplanes with provisions for obtaining a significant reduction in the one-engine-inoperative power-on stall speed; and

(3) 1.10 times VMC established under § 25.149.

(c) V2, in terms of calibrated airspeed, must be selected by the applicant to provide at least the gradient of climb required by § 25.121(b) but may not be less than --

(1) V2MIN;

(2) VR plus the speed increment attained (in accordance with § 25.111(c)(2)) before reaching a height of 35 feet above the takeoff surface; and

(3) A speed that provides the maneuvering capability specified in § 25.143(g).

(d) VMU is the calibrated airspeed at and above which the airplane can safely lift off the ground, and con- tinue the takeoff. VMU speeds must be selected by the applicant throughout the range of thrust-to-weight ratios to be certificated. These speeds may be established from free air data if these data are verified by ground takeoff tests.

(e) VR, in terms of calibrated airspeed, must be selected in accordance with the conditions of paragraphs (e)(1) through (4) of this section:

(1) VR may not be less than --

(i) V1;

(ii) 105 percent of VMC;

(iii) The speed (determined in accordance with § 25.111(c)(2)) that allows reaching V2 before reaching a height of 35 feet above the takeoff surface; or

(iv) A speed that, if the airplane is rotated at its maximum practicable rate, will result in a VLOF of not less than 110 percent of VMU in the all-engines-operating condition and not less than 105 percent of VMU determined at the thrust-to-weight ratio corresponding to the one-engine-inoperative condition.

(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 takeoff provisions.

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

(4) Reasonably expected variations in service from the established takeoff procedures for the operation of the airplane (such as over-rotation of the airplane and out-of-trim conditions) may not result in unsafe flight characteristics or in marked increases in the scheduled takeoff distances established in accordance with § 25.113(a).

(f) VLOF is the calibrated airspeed at which the airplane first becomes airborne.

(g) VFTO, in terms of calibrated airspeed, must be selected by the applicant to provide at least the gradient of climb required by § 25.121(c), but may not be less than --

(1) 1.18 VSR; and

(2) A speed that provides the maneuvering capability specified in § 25.143(g).

[Doc. No. 5066, 29 FR 18291, Dec. 24, 1964, as amended by Amdt. 25-38, 41 FR 55466, Dec. 20, 1976; Amdt. 25-42, 43 FR 2320, Jan. 16, 1978; Amdt. 25-92, 63 FR 8318, Feb. 18, 1998; Amdt. 25-94, 63 FR 8848, Feb. 23, 1998; Amdt. 25-108, 67 FR 70826, Nov. 26, 2002]




That should about do it........

[BOAC]

Well, that about covers it!!

Captain P - start by assuming it HAS been covered on pprune before! Search brings up this and

here and here and

here

A few links for you! Hope that is what you are looking for, if you mean 'definitions'. If you mean 'derivations' I think you'd do better on 'Flight Testing', since a lot of the speeds come from flight test material.

There are lots more links in 'search' but I fell asleep.

[m&v]

Try to borrow a copy of PJ.Swatton's Aircraft Performance Theory
The numbers and definitions are JAR orientated..
Cheers

[cumulus]

Since I have began ATPL theory, have been collecting V speeds.

Thank you gentlemen, a real treasure trove here..

[Captain Phaedrus]

Thanks all, especially 747FOCAL. Managed to get to the office and dig out the relevant bits in due time.

Yes, searching is a great idea, but here, the search title has to be greater than three characters long, so entering V2 is not possible. I did mean derivations, by the way! Thanks nonetheless for the info. Good reading.

m&v, I did, then leant it to 'a friend'...

cumulus, just take a reality check on the old 'Do I need to get a life?' question once in a while!!

Happy landings all!

CP

[OverRun]

Useful stuff all round. Thanks for the reference m&v - I've been wanting to get something like that for a while - amazon.co.uk has it in stock and that's the Xmas present to myself