Not sure if this helps.....
Aircraft performance should be such that, with an engine failure at V1, the aircraft will obtain a minimum of V2 by the screen height ( 35ft dry / 15 ft wet ). Nb. With all engines running, this is more likely to be V2 + 15 to 20 Kt.
In the configuration used for takeoff, V2 is never less than 1.1 x Vmca, OR 1.2 x stall speed. Thus, when at V2, the aircraft is (10%) above Vmca, and (20%) above the power-off stall.
Nb. Most piston engined aircraft have a V2 which is 15% above the power off stall speed, but with jet aircraft the benefit of prop wash over the wing is lost and so, to make up for this, the margin was increased to 20%.
You might recall ( from Perf’A )
The 1st segment begins at ‘reference zero’ and ends when gear retraction is complete wherein it assumes you have attained and maintained V2.
W.r.t. 1st segment climb gradients - BCARs/JARs require a minimum gross climb gradient in this segment of:
2 power units = 1.0%
3 power units = 0.7%
4 power units = 0.5%
Nb. If landing gear is fully retracted by 35ft, there will be no 1st Segment and the Take-off Flight Path will commence with the 2nd Segment….. starting at 35ft ( dry ).
Failing that, the 2nd segment climb begins at the end of the 1st segment and ends at a
minimum height of 400' above the runway and a
maximum height of 1500ft ( which also happens to be where the net take-off flight path normally ends ).
Aside - many company Airport Analysis / Performance table specify an acceleration altitude of 1000ft AGL ( the B737 FMC usually defaults to 1500ft )
V2 ( with gear 'Up' ) must be maintained throughout the 2nd segment to a minimum of 400 ft AGL, such that the 2nd segment climb performance criteria is met.
W.r.t. 2nd segment climb gradients - BCARs/JARs require a minimum gross climb gradient in this segment of:
2 power units = 2.4%
3 power units = 2.7%
4 power units = 3.0%
This is always the most restrictive climb segment for all two engine jets currently certificated. Nb. It may not be the most limiting for some older airplanes whose engines have a substantial difference between Take-Off, and Maximum Continuous power.
V2 is not ‘performance’ related but to do with the handling characteristics of the aircraft. Achieving and flying at V2 will assure that the aircraft performs as stated in the Aircraft Flight Manual (AFM). If an engine is lost at a speed greater than V2, you will be above the minimum required takeoff flight path ( .... think about it
).
V2 is not Vxse ( minimum ground distance to altitude / best angle single engine ) and neither is it Vyse ( minimum time to altitude / best rate single engine ) where these speeds are typically 20 to 70 knots higher respectively. Accordingly V2 is set as somewhat of a compromise between what would be optimum for takeoff ( suffering an engine failure at V1 ), and what would result in the most optimum initial climb performance.
V2 varies with weight and flap setting. Less flaps means better climb performance, but usually requires a longer runway ( .... again, think about it !
)