LESSON 13 Chapter 12 Takeoff Performance ANA Chapter 2

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Flight Theory

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

 

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