**Chapter 12**

- Takeoff Performance
- Takeoff Performance
- Important factors for takeoff performance:

–Takeoff velocity

- Affected by stall speed, minimum control speed (Vmc), thrust or power, CL values

–Acceleration

–Takeoff distance

**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
- Where:

– a = Acceleration

–V = Velocity at time t

–V0 = Velocity at time t0

- Change in velocity over change in time
- Linear Motion
- Making a few assumptions we can solve for velocity (V), distance (s) and average V (Vav)
- The formula we arrive at is :
- Where s = distance
- V = takeoff velocity
- a = acceleration
**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 roll.
- The angle of incidence is set for Dmin on larger transport type aircraft
- These type of aircraft have to rotate to generate lift
- Rolling friction is a constant on these aircraft
**Linear motion**- In our airplanes, there is some lift being generated during the takeoff roll.
- The second assumption is that thrust is increasing during the takeoff roll.
- In our airplanes this is not true because of the decreasing 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 (fps2)
- Fn=net acceleration force(lb)
- m=mass, slugs (W/g)
- OR
- In the second equation:
- W=weight
- g=gravitational acceleration (32 fps2)
- T=thrust
- D=drag
- F=rolling friction
**Factors Affecting Takeoff Performance**- 1. Aircraft gross weight
- 2. Thrust
- 3. Temperature
- 4. Pressure altitude
- 5. Wind direction and velocity
- 6. Runway slope
- 7. Runway surface
- Takeoff Eh
- Got to off load some back bacon to decrease the takeoff
- To figure the affect of a change in weight, altitude, or wind use this equation:
- Subscript 1 is starting condition
- Subscript 2 is new condition
**Effect of Weight Change**- Increasing the gross weight effects the aircraft 3 ways:
- 1. the velocity needed to takeoff is increased
- 2. there is more mass to be accelerated
- 3. there is more rolling friction
**Effect of Weight Change**- We can use the formula:
- Therefor we can see that takeoff velocity varies as the square of the weight.
- Double the weight and V has to quadruple
**Effect of Weight Change**- Extra weight has a twofold effect on acceleration
- First, with more mass 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.

- Second, 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 vurses a sports car.
- The David Cushing memorial mistake.
- 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:
- 1. A higher takeoff velocity is required (TAS)
- 2. 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
- σ2 = altitude density ratio
**Effect of Altitude**- For every 15˚F or 8.5˚C density altitude is increased or decreased by about 1000 feet
- For every 20˚F 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 equations that express this are:
- Headwind
- Tailwind
- 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 or tailwind
- 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.
- For us that would be about 6 kts
- The effects of as little as a 2˚ 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
- The rule of thumb here is add 5% to s for each percent of uphill slope
- The problem with this rule is degrees are given in the AFD not percent slope so you have to convert
**Aborted Takeoffs**- Definitions pg 185 Dole
- For twin engine aircraft, charts are published to determine exactly how much runway is needed
- Accelerate Go and Accelerate Stop charts are included in modern POH’s
- These charts account for density altitude, weight, wind conditions, and pilot reaction times
- We do not have these for singles
- However, we can use our takeoff distance and landing distance charts to come close
- Multiengine discussion:
- Accelerate stop distance
- Vmc talk
- 1. definition
- 2. arm and moment
- 3. p factor
- 4. critical engine (left)
- 5. lateral cg loading
- 6. Rolling moment induced by rudder
- 7. Zero side slip