# LESSON 13 Chapter 12 Takeoff Performance ANA Chapter 2

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:
•
•
• 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)