Mathematics behind V1, VR, V2 calculation

[NoutvanZon]

Hi Guys,

Does anyone know the algorithm behind V1, VR and V2 calculation? Given that you know the wind heading and speed, the aircraft gross weight and all other relevant variables.

I'm not searching for tables of info to look for the speed myself. I want to set up some php calculations for fun and see if I can calculate the airspeeds accurately.

Cheers,

Nout

[Pete_SMS]

Hey,

there is no generic algorithm for V1, V2 and Vr. These speeds will be different for every aircraft. Developers might have "internal" equations for calculating V1, V2 and Vr, in order to produce aircraft specific data tables, charts etc. or they might even have computer programs which pilots can use before a flight. However, this data is only related to that particular aircraft.

As you probably know, V1 is the maximum speed for a rejected takeoff or the minimum speed at which you could continue the takeoff, if you have an engine failure. So therefore V1 strongly depends on the acceleration-stopping performance of the aircraft.

Vr will be a speed that is selected in a way that the aircraft will be able to reach V2 before it will arrive at a height of 35 ft abouve ground level. This also strongly depends on specific aircraft performance.

V2 considered as the T/O safety speed, will be used for the initial climb in case an engine is lost before reaching V2 and as V1 and Vr strongly aircraft dependent.

So there is no generic algorithm valid for any kind of aircraft. Pilots often use rules of thumb to memorize these numbers for different T/O weights, runway and wind conditions etc., but not really something you are looking for.

I hope this helps. If not, please be a little more specific with your question.

-Pete

[NoutvanZon]

Good Evening Pete,

Thanks for your very detailed answer. Answered my question very nicely! I guess I will have to dig deep into charts throw the data into a database maybe..

Nout

[YYZatcboy]

it also depends alot on station pressure and wind.

[Lukasz]

I've found this method of calculating/estimating V speeds:

http://www.b737.org.uk/vspeedcalc2.htm

There is another interesting information here:

http://www.pprune.org/archive/index.php/t-124286.html

3. V2 begins and ends at V2 for any particular departure. Any deviation from the SELECTED V2, is a V2 plus or V2 minus deviation. Considering that V2 is the speed to which the aircraft, with one engine inop, must accelerate after rotation at Vr and lifting of at Vlof appropriate to the prevailing conditions, then V2 selection may begin at V2min which is the lowest speed that V2 may be in any ambient conditions or any configuration. In terms of CAS V2min may not be less than:

i) 1.2 Vs for:

a) Two and three-engined turbo-prop a/c and,

Turbo-jet a/c without provisions for obtaining a significant reduction in the one engine inop stalling speed.

ii) 1.15Vs for:

a) Four-engined turbo-prop a/c and

Turbo-jet a/c having provisions for obtaining a significant reduction in the one engine inop stalling speed.

iii) 1.10Vmc. JAR 25.107(

V2max (if you will) may be selected under the correct prevailing conditions, and would then be, V2 at Flap 0 taking into account all of the above: therefore the CONFIGURATION criteria is stated. It is of course worth bearing in mind that regardless of which V2 is selected for a particular departure, it needs to meet the above criteria AND then remains V2 for that take-off.

4. Once Flap retraction is commenced, the acceleration segment (and the basic principles of flight on most large aircraft) does not allow for V2 to be maintained. Therefore, V2 is also defined as the target speed to be attained at the screen height with one engine inoperative and is maintained to the point where acceleration to Flap Retraction Speed is initiated.

[Morten XPFW]

..and acft model  length.  Example a B737-800 will have a higher Vr/V2 than a B737-700

for the same weight to avoid tailstrike...