# Takeoff Field Length (Bizjet)

Three decision speeds are worked out to establish the V1 for the BFL computation. Equation 13.2 gives average acceleration as:

a = g[(T/ W – ,i) – (CLSq/ W)(Cd/Cl – n)]

 Flap setting (deg) 0 8* 20* Landing* CDpmin 0.0205 0.0205 0.0205 0.0205 CLmax 1.55 1.67 1.90 2.20 A CDflap 0 0.013 0.032 0.060 A cD-U/c 0.0222 0.0220 0.0212 0.0212 A CD^ne^ng (fuselage-mounted) 0.003 0.003 0.003 0.003 A CD^ne^ng (wing-mounted) 0.004 0.004 0.004 0.004 Rolling-friction coefficient, p 0.03 0.03 0.03 0.03 Braking-friction coefficient, pB 0.45 0.45 0.45 0.45 Vstall @20,680 lb (ft/s) 186.5 179.6 168.4 – VR (kt) (multiply 1.688 to obtain ft/s) 112 (189) 104 (175.5) – V2 (kt) (1.688 ft/s) 128.2 (216.5) 124.8 (210.7) – T/W (all-engine) 0.32 0.32 – T/W (single-engine) 0.16 0.16 – CD/CL at ground run (all engine) 0.1 0.1 – CD/CL at ground run (one engine out) 0.102 0.102 –

* Takeoff at 8- and 20-deg flaps. Landing at 35- to 40-deg flap, engines at idle, and Vstaii at aircraft landing weight of 15,800 lb.

The average acceleration a is at 0.7V of the segment of operation. For each segment of the BFL, a is computed.

The lift coefficient during the ground run is changing with speed gain and is not easy to determine. During the ground run, the angle of attack is low, even when the aircraft reaches the stall speed, Vstall. Up to the decision speed V;, only a fraction of the aircraft weight is taken up by the wing as a result of lift generation. Liftoff is not achieved until a pilot rotates the aircraft just above the Vstall. There is a rapid gain in lift generation because the angle of attack increases rapidly with rotation. Table 13.9 lists typical CL and CD/CL values.

Segment A: All Engines Operating up to the Decision Speed V1

Using Equation 13.2 and data from Table 13.6, the average acceleration becomes:

a = 32.2 X [(0.34 – 0.03) – (Cl?/64)(0.1 – 0.03)] = 32.2 x (0.31 – Ctq/914.3)

At a representative speed of 0.7V;, the average q = 0.5 x 0.002378 x 0.49V;2 = 0.0006 x V;2. At this segment, the average CL = 0.5 (yet to reach the full value). Then:

a = 32.2 X (0.31 – Cq/914.3)

= 32.2 x (0.31 – 0.0003 x V2/914.3) ft/s2

Table 13.9. Bizjet takeoff aerodynamic coefficients (from experiments and statistics)

 Average CL Average CD 8-deg flap From V0 to V1 0.4 0.031 *From V1 to VLO 0.4 0.035 *From VLO to V2 (20-deg flap) 1.9 not used (see example)

* One engine inoperative

Equation 13.3 gives the ground distance covered as:

Sg = Vave x (V/ – Vi)/a

Table 13.10 computes the ground distance covered for all engines operating up to V1 .

Segment B: One-Engine Inoperative Acceleration from V1 to Liftoff Speed, VLO

Because one engine is inoperative, there is a loss of power by half (T/W = 0.17) plus an asymmetric drag rise (CD/CL = 0.102). As the speed increases, the aver­age CL increases to 0.8, making the weight on the wheels lighter; therefore, the ground friction, /л, is reduced to 0.025. The acceleration Equation 13.2 is rewritten as follows:

a = 32.2 x [(0.17 – 0.025) – (Cl^/64)(0.102 – 0.025)] = 32.2 x (0.145 – 0.8 x q/831.2)

The velocity that would give the average acceleration is:

V0.7 = 0.7 x (Vlo – V1) + V1

a = 32.2 x (0.145 – 0.000951 x Vi.72/831.2 = 32.2 x (0.145 – 0.00000114 x V027) Equation 13.3 gives the ground distance covered as:

Sg = Vave x (Vf – Vi)/a

Table 13.11 computes the ground distance covered from Vi to VLO for the two flap settings.

Table 13.11. Segment B: Bizjet one-engine ground distance Vi to VLO (8-degflap)

Guess V1 (kt) (1.688 ft/s) 90 (151.92)

Vstaii at 20,600 lb (ft/s) 177.6

VLo at 1.12 Vstaii 199

V0.7 = 0.7 x (VLO – V1) + V1 (ft/s) 185 (0.166M) T/W (from Figure 13.1) 0.138

q (dynamic head at 0.7V1) 41.09

a (ft/s2) 3.21

Ground distance, SG_VLO (ft) 2,664

 Guess V1 (kt) (1.688 ft/s) 90 (151.92) 100 (168.8) 110 (185.7) Flap (deg) 8 8 8 Vstall (kt) (ft/s) 179.6 179.6 179.6 Vlo at 1.12 Vstaii 200.5 200.5 200.5 V2 at 1.2 Vstall 215.52 215.52 215.52 Vave (ft/s) [(Vlo + V2)/2 + Vlo] 208 208 208 Flaring distance in 3 s, SG_V2 (ft) 624 624 624 Segments (B + C) 3,288 2,505 1,575 TOFL (Sg_vi + Sgvlo + Sgv2) 4,655 4,240 3,717

Segment C: Flaring Distance with One Engine Inoperative from VLO to V2

The flaring distance reaches V2 from VLO; from statistics, the time to flaring is 3 s. Table 13.12 computes the ground distance covered from VLO to V2 with one engine inoperative for the two flap settings. In this segment, an aircraft is airborne; hence, there is no ground friction. Taking the average velocity between V2 and VLO gives the distance covered during flare.

The next step is to compute the stopping distance with the maximum application of brakes.

Segment D: Distance Covered in 1 s as Pilot-Recognition Time and 2 s for Brakes to Act from V to VB (Flap Settings Are of Minor Consequence)

Table 13.13 computes the ground distance covered from Vi to VB.

Segment E: Braking Distance from VB to Zero Velocity (Flap Settings Are of Minor Consequence)

The reaction time to apply the brakes, after the decision speed, V1t is 3 s. The aircraft continues to accelerate during the 3 s.

For an aircraft in full braking with pB = 0.4, all engines shut down, and the average CL = 0.5, Equation 13.2 for average acceleration, based on 0.7VB (« 0.7V1), reduces to:

a = 32.2 X [(-0.4) – (Ciq/64)/(0.1 – 04)] = 32.2 x [-0.4 + (0.15q/64)]

= 32.2 x [-0.4 + q/426.7)] = 0.075q – 12.88

Table 13.14 computes the ground distance covered from VB to stopping.

The TOFL (see Table 13.12, Segments A + B + C) and the stopping distance (see Table 13.14, Segments A + D + E) are plotted in Figure 13.11 to obtain the BFL for a flap setting of 8 deg and summarized in Table 13.16. It satisfies the specified TOFL requirement of 4,400 ft.

Table 13.13. Segment D: Bizjet failure-recognition distance

 Estimate V1 (kt) (1.688 ft/s) 90 (151.92) 100 (168.80) 110 (185.70) Distance in 3 sec at V1, SGb (ft) 456 506 557