**Chapter 12**

**Takeoff Performance**

## Important factors in takeoff performance

- Takeoff velocity
- The acceleration during takeoff
- The distance required to complete the takeoff

## Linear motion

If given a constant acceleration, for a given change in velocity there will be a corresponding change in time.

This can be expressed by the formula: pg179

Making a few assumptions we can solve for velocity (V), distance (s) and average V (Vav)

## Linear motion

Newton’s second law explains the relationship here F=ma.

The force providing the acceleration of course is the unbalanced thrust force.

The figure on pg181 in Dole shows forces on an airplane during takeoff.

This figure makes the assumption that there is no lift being generated during the takeoff role.

## Linear motion

In our airplanes, there is some lift being generated during the takeoff role.

The second assumption is that thrust is increasing during the takeoff role.

In our airplanes this is true because of the angle of attack on the prop.

When figuring acceleration one must take into account the thrust the drag the rolling friction, and the weight.

Linear motion

The equation is:

Where a=acceleration (fps^{2})

Fn=net acceleration force(lb)

W=weight

g=gravitational acceleration (32 fps^{2})

m=mass, slugs (W/g)

## Factors Affecting Takeoff Performance

- Aircraft gross weight
- thrust
- temperature
- pressure altitude
- Wind direction and velocity
- Runway slope
- Runway surface

## Takeoff Eh

To figure the affect of a change in weight, altitude, or wind use this equation:

## Effect of Weight Change

Increasing the gross weight effects the aircraft 3 ways:

- the velocity needed to takeoff is increased
- there is more mass to be accelerated
- there is more rolling friction

## Effect of Weight Change

First, we can use the formula:

Therefore we can see that takeoff velocity varies as the square of the weight.

## Effect of Weight Change

Second, there is more rolling friction, for an extra 1000 lbs, with a coefficient of friction of .03, an extra 30lbs of rolling friction would be added.

Third, Acceleration is inversely proportional to the mass (or weight) of the aircraft.

## Effect of Weight Change

Most of the problem is going to be not with the rolling friction but with the acceleration of the extra mass.

Think about a truck verses a sports car.

So, the effect of a weight change on takeoff distance is:

If the airplane is 10% over the weight for a given value the takeoff run will be 21% longer

## Effect of Altitude

Dole points out that the runway temp may be higher than official airport temp.

An increase in density altitude has a twofold effect on takeoff performance:

- A higher takeoff velocity is required
- Less thrust is available

less power, less thrust by the prop and wings are less effective

## Effect of Altitude

It takes a higher true airspeed when density altitude is higher.

Thus taking into account that thrust is decreased in normally aspirated engines approximately the same amount as the density decreases, the equation is:

## Effect of Altitude

For turbo charge engines there is no decrease in power so the equation is:

Where s1 = standard sea level takeoff distance

s2 = altitude takeoff distance

sigma2 = altitude density ratio

## Effect of Altitude

For every 15F or 8.5C density altitude is increased or decreased by about 1000 feet

For every 20F increase in temperature, the ability of a parcel of air to hold water vapor doubles.

The given air density would decrease 2% to 3% as a result.

The engine is most effected and may loose up to 12% power in this situation.

## Effect of Wind

A headwind means a lower takeoff groundspeed than calm wind conditions.

This means that acceleration over the ground is less, however acceleration through the airmass is the same.

## Effect of Wind

The equation that expresses this is:

Where s1 = standard sea level takeoff distance

s2 = altitude takeoff distance

1 = ratio of acceleration through the airmass with and without wind

Vw = velocity of the headwind

V1 = no wind takeoff velocity

## Effect of Runway slope

When an aircraft takeoff includes runway slope the component of weight parallel to the runway will cause a need for an increase in accelerating force.

There is always a question of whether to take off up hill or into the wind.

This depends on the amount of slope and the strength of the wind.

## Effect of Runway slope

So what do you think eh?

It is almost always better to takeoff upwind and up hill if the headwind component is 10% or more of your takeoff speed.

The effects of as little as a 2degree upslope on a 3,000 pound airplane the rearward component of weight has a value of 105 lbs.

This is a significant value when compared to the thrust of only 865 lbs

## Aborted Takeoffs

Definitions pg 185 Dole

## Multiengine discussion:

Accelerate stop distance

Vmc talk

- definition
- arm and moment
- p factor
- critical engine (left)
- lateral cg loading
- Rolling moment induced by rudder
- Zero side slip