Take-Off Field Length
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
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
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
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
dV = a dt and dx = V dt = V/a dV
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
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
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.