Take-Off Field Length

Introduction

Although the take-off field length may seem like a performance characteristic of secondary importance, it is very often one of the critical design constraints. If the required runway length is too long, the aircraft cannot take-off with full fuel or full payload and the aircraft economics are compromised.

For example, In some cases aircraft take-off from San Jose and fly all the way to San Francisco (about 40 miles) before making their first refueling stop. This is because the field length is insufficient to take-off with full fuel in San Jose and the tanks are topped off at SFO where the runways are longer. Since this kind of operating restriction is not desirable, the aircraft is designed to meet take-off field length requirements for selected airports with full payload and fuel.

This constraint often sets the aircraft wing area, engine size, or high lift system design.

To compute the required take-off distance, we consider the take-off profile shown below.

Important Speeds

The following speeds are of importance in the take-off field length calculation:

Vmu Minimum Unstick Speed. Minimum airspeed at which airplane can safely lift off ground and continue take-off.

Vmc Minimum Control Speed. Minimum airspeed at which when critical engine is made inoperative, it is still possible to recover control of the airplane and maintain straight flight.

Vmcg Minimum control speed on the ground. At this speed the aircraft must be able to continue a straight path down the runway with a failed engine, without relying on nose gear reactions.

V1 Decision speed, a short time after critical engine failure speed. Above this speed, aerodynamic controls alone must be adequate to proceed safely with takeoff.

VR Rotation Speed. Must be greater than V1 and greater than 1.05 Vmc

Vlo Lift-off Speed. Must be greater than 1.1 Vmu with all engines, or 1.05 Vmu with engine out.

V2 Take-off climb speed is the demonstrated airspeed at the 35 ft height. Must be greater than 1.1 Vmc and 1.2 Vs, the stalling speed in the take-off configuration.

Further information on these design speeds are given in the relevant sections of FAR part 25, including those dealing specifically with take-off and also those dealing with control requirements.

FARs related to take-off
FARs related to control

Estimating the Required Field Length

The calculation of take-off field length involves the computation of the distance required to accelerate from a stop to the required take-off speed, plus a climb segment. Since the acceleration distance is typically about 80% of the total distance, we first consider this portion.

The distance required to accelerate to the speed Vlo can be computed by noting that:
dV = a dt and dx = V dt = V/a dV
so:

If the acceleration is assumed to vary as: 1/a = 1/a0 + kV2 then:

So, we could either integrate the acceleration numerically or use an average value, computed at .70 of the lift-off speed.

Ignoring the small speed change between lift-off and the 35 ft screen height, we can take Vlo = 1.2 Vs. Then, Vlo = 1.2 (2 W) / (rS CLmax).

With, a = F/ m = T-D / m (where T=Thrust, D=total drag including ground resistance, m=take-off mass), the expression for acceleration distance becomes:
x = 1.44 W2 / (g r S CLmax (T-D))

This expression is not very useful directly because it is difficult to estimate the drag, and we must add the climb portion of the take-off run. More importantly, commercial take-off distances assume engine failure at the worst possible time. If the engine fails sooner, the pilot can stop in a shorter distance. If the engine fails at a higher speed, the airplane can continue the take-off and reach a height of 35 feet in a shorter distance. This worst time corresponds to the critical engine failure speed VEFcrit. It is assumed that the pilot recognizes the engine failure and takes action a short time* later, at which time the speed is called the decision speed, V1. At a speed higher than V1, the pilot must continue the take-off; at a lower speed he or she must stop.

The commercial take-off problem is very complex, involving acceleration on all engines, acceleration with one engine inoperative, deceleration after engine failure, and climb with one engine inoperative. This means that the design of spoilers, braking system, and rudder will affect the FAR take-off field length.

The preliminary design computations, therefore, include correlation of the primary design parameters with actual demonstrated performance. The correlation parameter is closely related to that which appears in the simple analytical analysis on the previous pages. Examples of the correlations for take-off field length with engine failure are shown in the figure below. The propeller data is much more uncertain due to variations in propeller efficiency.

The FAA take-off field length in some cases may be set, not by the field length based on engine failure, but on the all-engines operating performance. If the all-engines runway length multiplied by 1.15 exceeds the 1-engine-out field length, the larger value is used. For four-engine aircraft the all engines operating condition times 1.15 is usually critical.

Fits have been made to the FAR field length requirements of 2,3,and 4 engine jet aircraft vs. the parameter:


W is the take-off gross weight (lbs).

Sref is the reference wing area (sq ft).

s is the ratio of air density under the conditions of interest which might well be a hot day in Denver or another high altitude airport.

CLmax is the aircraft maximum lift coefficient in the take-off configuration.

T is the total installed thrust (all engines running). It varies with speed and must be evaluated at 70% of the lift-off speed which we take as 1.2 Vs. The variation of thrust with speed shown here may be used for this calculation if detailed engine data is not available.

For 2 engine aircraft: TOFL = 857.4 + 28.43 Index + .0185 Index2
For 3 engine aircraft: TOFL = 667.9 + 26.91 Index + .0123 Index2
For 4 engine aircraft: TOFL = 486.7 + 26.20 Index + .0093 Index2

Since for four engine aircraft, the all-engines operating (with 15% pad) case is critical, one may use this fit for the all-engines operating case with 2 or 3 engines as well. Note that the 15% markup is already included.



The figure below illustrates the installed thrust vs. speed for a number of engine types for use in this calculation.


When an aircraft is limited to a certain angle of attack on take-off, other considerations may apply. This is especially true for supersonic designs with low aspect ratio and high sweep. See the additional discussion at this link.