Aircraft Performance

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Commercial Ground School AVF 221

Aircraft Performance

Altitude, Temp and Pressure
Air density is measured in slugs per cubic foot and at sea level equates to .002378
Pressure is measured in inches of mercury, millibars or psf at sea level this equates to 2116psf
Temperature is measured in F or C but must be converted to Rankin or Kelvin for our equations at sea level this equates to 59° F, 15° C or 519° R, 288° K

Altitude, Temp and Pressure
In our lift equation s (sigma, density ratio) accounts mathematically for pressure and temperature effects on lift
Pressure ratio (delta) is derived by dividing current pressure by sea level standard pressure of 2116 psf
Temperature ratio (theta) is derived by dividing current temperature in Kelvin by the sea level standard day temp of 288° K
Density ratio is found by taking delta divided by theta

Altitude, Temp and Pressure
Pressure altitude is the measurement in feet of the location of the standard datum plane of 29.92
This is why when we set our altimeter to 29.92 is shows us the altitude of its location
Density altitude is the altitude in the standard atmosphere corresponding to a particular value of air density
We get from here to there by compensating pressure altitude for non-standard temperature
This is what the equation shows
This allows us to pin a number on a specific density
Which in turn allows us to relate aircraft performance to these numbers
The equation also shows relationships
Density varies directly with pressure
More pressure = more density
Density varies inversely with temperature
More temperature = less density

Altitude, Temp and Density
There are some other items that should be considered that drive up density altitude not in the equations
High humidity upwards of 95% or higher can decrease density 2 to 3%
This has a negligible effect on lift but Hp may decrease up to 12%
The complete list:
High elevation
High temperature
High humidity
Low atmospheric pressure
Altitude, Temp and Density
If you don’t have a chart handy or your E6b a rule of thumb for density altitude is for every 15°F or 8.5°C density altitude is increased or decreased by about 1000 feet

Takeoff performance
1. Aircraft gross weight
2. Thrust
3. Temperature
4. Pressure altitude
5. Wind direction and velocity
6. Runway slope
7. Runway surface

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
Double the weight and velocity has to quadruple

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.
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
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 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.
At higher density altitudes, the effect will be more since less thrust is available
If the headwind component is 10% or more of your takeoff speed, it’s better to takeoff into the wind and uphill
If winds are less than 10%, takeoff downhill
Either way if you don’t have 70% of your lift off speed by the half way point abort the takeoff

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.
Wind effects the takeoff in both time and distance
If the wind is 25% of the takeoff speed, distance is only 58% of the no wind value, not 75% as you might think
Never underestimate the effect of wind

Takeoff Rule of Thumb
Add 12% for every 1000 feet of pressure altitude above sea level
Add 12% to that for every 15°F or 8.5°C above standard temp
Weight effects are at the square so for 10% weight change takeoff roll is 21%

Forces in a Climb
Lift is less than weight in a climb.
The thrust can be broken into two vectors one of which is a vertical component.
This is what offsets the value of lift that is less than weight.

Climb Performance
Vy or max rate of climb occurs at the velocity where max excess power occurs (THP).
In other words the greatest difference between horsepower available and horsepower required.
Max rate of climb would be 0 at stall and 0 at max level speed
At both these points excess THP is near 0
Because it takes excess THP to climb, these would not be good speeds to use

Climb Performance
Vx or max climb angle is achieved when excess thrust is at a max.
In order to pin down an airspeed, one must calculate the sine of the corresponding climb angle then plot it against the velocity.
This will be where the greatest thrust component exists to move the plane up
The example shows max climb at stall for the prop whereas the jet is at L/Dmax

Climb Performance
As altitude is gained Vy drops 1% per 1000 feet
As altitude is gained Vx increases .5% per 1000 feet
They meet at the absolute ceiling
At this point you have neither excess thrust or power

Specific Range
To obtain max distance, the specific range must be at a max the equation is:


The tangent line drawn to the thrust horsepower required curve should indicate the max specific range velocity.
For a prop aircraft this is L/Dmax

2 things occur at L/Dmax for a prop plane:
1. Max glide ratio
2. Max range
L/D max is located at the tangent!
For the Bonanza this is 105kts

To obtain max endurance the min fuel flow is required to stay airborne the max amount of time.
Minimum power required should be the point of minimum fuel flow
This is not L/Dmax
It is also not the slowest speed because of the increase in induced drag
This is found at the bottom of the Pr curve
A good rule of thumb is use 1.2 Vs
If you’re in a retract use 1.3 Vs
This would be about 83kts in the Bonanza

Minimum Sink
This speed is designed to give the least amount of descent rate
This may be the go to speed for an engine out glide at night where you are unsure of the terrain features
Single engine, fixed gear 1.1 Vs
Single engine, gear retracted 1.2 Vs
Multiengine, gear retracted 1.3 Vs
For the Bonanza this would be about 77kts

Best Glide
Designed to give the greatest distance per altitude loss
Occurs at max L/D
Altitude has minimal effect on glide distance
A higher TAS at altitude will move the aircraft faster down the glide path
The glide path however doesn’t change provided the correct IAS is used for the weight
ght does change the airspeed but distance remains the same
As weight decreases so does glide speed

Landing Performance
Remember that the approach speed is usually not the absolute minimum speed.
It may have factors such as weight, stall speed, minimum controllable speed, TA vs TR or PA vs PR added in
Most GA airplanes have a factor of 1.3Vso
That equates to 130% of the stall speed in the landing configuration
On the approach the prop plane will have an advantage in that thrust is readily available almost immediately and induced airflow will provide some lift

Landing Distance
You can think of the landing distance in terms of kinetic energy that must be dissipated before the airplane is stopped.
Remember, mass is in slugs and velocity is in fps:

You can dissipate energy by using the brakes, aerodynamic braking or by transferring the energy into the ground
In fact, if you transfer enough energy into the ground, you can shear off the gear and really shorten your landing distance
So after your next less than perfect touch down just tell your instructor you’re dissipating the KE for a shorter roll out
In an emergency landing, shearing off wings and/or gear may dissipate the KE and reduce the g forces to a survivable level
Which is why you almost always want to land gear down

Landing Distance
Landing distance is directly affected by weight
Double the weight and double the landing distance
While the effects of velocity are more pronounced
Double the landing speed and quadruple the energy to be dissipated
A 10% increase in landing speed will result in at least a 21% greater landing distance

Landing Distance
Altitude does not effect the landing as much as the takeoff
TAS goes up 2% per 1000 feet
As your density altitude goes up so does the distance to stop because of the increase in velocity
Temperature affects your landing roll by driving up density altitude
For every 15°F above standard add 4% to the landing roll
If the runway has a slope, land uphill
A 5° slope would give a 3000lb airplane a retardant force of 261lbs

Forces on Aircraft during landing
Heavy aircraft do not use much aerodynamic braking.
The large mass of these airplanes need a more effective way to stop in a short amount of space.
Therefore thrust reversers and anti skid brakes are used

There are 3 types of hydroplaning
1. Dynamic
2. Viscous
3. Reverted rubber

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