SIZING OF AIRCRAFT ACCORDING TO TAKEOFF DISTANCE REQUIREMENT

SIZING OF AIRCRAFT ACCORDING TO    TAKEOFF           DISTANCE REQUIREMENT

The take off ground run (S_TOG) of an aircraft is proportional to takeoff  wing loading (W/S)_TO, or  take off power loading (W/P)_TO . and maximum take off  lift C_Lmax  .

i.e,             S_TO a  ( (W/S)_TO* (W/P)_TO ) / (sC_Lmax) = TOP    ——-(1)

     this equals to TOP (take off parameter ) and its dimension  is  newton²/ m²hp .

As we know that the coefficient of lift at take off is typically 1.21 times maximum lift coefficient.

So we can write it as a C_TO = C_LmaxTO  / 1.21

Below Fig relates S_TOG to the  take off parameter . for a range of aircraft of single and twin engine (source by aircraft flight dynamics and automotive flight control , Roskam.).

This graph suggest following relationship

                     S_TOG  = 4.9 TOP +0.009TOP²               _{———————}(2)

And , fig  Below  implies that ,

S_TO = 1.66 S_TOG                               ————(3)

   NOW from above two equation we get,

                          STO = 8.134 TOP + 0.0149 TOP²         ———–(4)

THIS EQUATION are generated on the basis of data from FAR 23 aircraft.

For the calculation for jet aircraft we might replace (W/P) TO (W/T).

Here is one example so that the above concept will clear to everyone.

For a given aircraft (take propeller driven) it is specified that S_TOG LESS THAN 1000m and S_TO IS LESS THAN 1500m at an altitude of 5000 ft  in standard atmosphere.

Equation (3) stipulates that ,

S_TO < 1660m

This clearly violate the second requirement. So for both takeoff requirement to be met it is necessary that ,

1500 = 8.134TOP + 0.0149 TOP²

FROM this we get TOP = 145.6

Since s = 0.8616 at 5000 ft , now put this values in eq—-(1) it translate into ( (W/S)_TO* (W/P)_TO ) / (C_Lmax) < 145.6 *0.8616

Now by putting the values of  (C_Lmax)   and  (W/P)_TO we get approximate value of (W/S)_TO  

SIZING OF AIRCRAFT ACCORDING TO MANEUVARING REQUIREMENT

SIZING OF AIRCRAFT ACCORDING TO MANEUVARING REQUIREMENT

In this post I am going to introduce about the sizing of aircraft according to their maneuvering requirement .

Specific requirement for sustained maneuvering capability (including sometimes specific turn rate) are often contained in the mission specification for agricultural ,aerobatic or for military aircrafts.

Sustained maneuvering requirement are usually formulated in terms of a combination of sustained load factor (n) at some speed and altitude.

The sustained maneuvering capability of an aircraft depends strongly on its maximum lift coefficient and on its trust.

For equilibrium in vertical direction of flight , it Is necessary that:-

n*W =C_L*q*S       ———–(1)

where n= load factor and, q= dynamic pressure

the maximum load factor can be capability of an aircraft (n_max)can be found from above equation(1) ;

n_max = C_L*q /(W/S)

this load factor can be sustained as long as there is sufficient thrust, since:-

THRUST = DRAG

T= C_DO + KC_L²,

T= (q*C_D0*S )+( C_L²*q*S/∏e*A.R)

After dividing above equation by W  we get :-

T/W = (q*C_DO/(W/S)) + (W/S)(n_max)²/(∏*e*A.R )

NOW,

If some maximum load factor is desired on a sustained basis at a given speed and altitude then , the above equation can be used to find out the relation between (T/W) and (W/S) for a given value of c_d0.

so we can find out the wing loading for a specific thrust by weight ratio and hence design the wing /aircraft accordingly.

If requirement is includes some specific turn rate then the following equation might be helpful:-

                            Turn rate= g(n²-1)^1/2/V