Why does having a geometry-limited aircraft lead to lower VLOFs?

Question

For this question, please have in mind these excerpts from the 14 CFR 25.107 - Takeoff speeds.

"(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."

and VR must be:

"(iv) A speed that, if the airplane is rotated at its maximum practicable rate, will result in a VLOF of not less than —

(A) 110 percent of VMU in the all-engines-operating condition, and 105 percent 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 airplane (i.e., tail contact with the runway), 108 percent of VMU in the all-engines-operating condition, and 104 percent of VMU determined at the thrust-to-weight ratio corresponding to the one-engine-inoperative condition."

My question is: why does having a geometry-limited aircraft lead to lower VLOFs? Is it because, since the aircraft cannot reach the angle of stall because of its limitation, the VMU for such airplanes is greater than the stall speed, and thus the maximum Lift Coefficient has not been reached and therefore it offers a higher safety margin regarding stall?

Answer 1

Unless someone can find an old 14CFR Part 25 ruling that has the explicit reasoning, I believe you are right to consider that the rationale for giving extra performance credit to airplanes that have demonstrated minimum unstick speed ($V_{MU}$) limited by tail contact is that they are not limited by aerodynamics. However, I should point out that the intent is to reduce the rotation speed ($V_R$) and not $V_{LOF}$, which is not a performance V-speed.

For Part 23 aircraft, which does not require $V_{MU}$ testing, 14CFR 23.51(c)(2) (pre Admt 23-64) requires $V_R$ to be no less than 1.10$V_{S1}$, or 110% of the stall speed for takeoff configuration obtained out of ground effect.

This mirrors the Part 25 requirement of 14CFR 25.107(e)(1)(iv)(A), which you have cited in the OP. The difference between the two is that Part 25 allows the applicant to lower the $V_R$ by taking credit for the ground effect and the rate of rotation, but also poses additional onus on the applicant to flight test the $V_{MU}$ (which is involved and high-risk).

Vmu can be limited by either:

• Stall in ground effect, or
• Stick pusher in the takeoff phase, or
• AOA limiter (FBW only) in the takeoff phase, or
• Tail contact with the ground (i.e. geometry limited).

In the last case, the aerodynamic capability of the airplane has not been reached. Therefore, 25.107(e)(1)(iv)(B) extends some credit to reduce the rotation speed. However, as specified in AC 25-7C, this credit can only be taken if the airplane is actually shown to be geometry limited from 96% to 100% of the lift-off speed ($V_{LOF}$) with the lowest thrust-to-weight ratio allowed for takeoff.