Power Curves

Power Curves

Aims and Objectives
  • To describe the four forces on an aircraft and how they relate to each other with respect to climb performance
  • Given specific performance parameters, derive:
    • thrust required
    • thrust available
    • power required
    • power available
  • Gain an understanding of the aerodynamic factors that derive Vx and Vy speeds for an aircraft

Revision

Drag
  • We know that there are two types of drag acting on an aircraft:
    1. Induced Drag
    2. Parasite Drag
  • As airspeed increases:
    • Induced Drag decreases
    • Parasite Drag increases
    • and vice versa
  • The change in both types of drag is non-linear with respect to airspeed
  • The force of Drag opposes the force of Thrust

Revision

Drag
  • As airspeed increases, Induced Drag decreases
  • As airspeed increases, Parasite Drag increases

Drag Curve 1

Revision

Drag
  • We can add the Induced Drag to the Parasite Drag
  • This will give us the Total Drag

Drag Curve 2

Revision

Drag
  • We can plot the Total Drag on the same graph
  • Over airspeed, the Total Drag initially decreases, then increases

Drag Curve 3

Revision

Climbing
  • In straight and level flight, Lift = Weight
  • However, to produce a climb, we use thrust
  • We apply extra thrust to what would otherwise maintain straight and level flight — excess thrust
  • Specifically, the vertical component of that excess thrust causes an aircraft to climb

Revision

Propellers
  • A propeller generates a force by rotating propeller blade(s)
  • The propeller blades generate a lifting force (thrust) by pitching at an Angle of Attack

Propeller Blade AoA 1

Revision

Propellers
  • As an aircraft travels forward, the resultant relative air flow on the propeller changes angle
  • This reduces the Angle of Attack of the propeller blades, producing less thrust

Propeller Blade AoA 2

Thrust Available

Propellers

Or in other words, as airspeed of a propeller-driven aircraft increases,

the Thrust Available decreases

Thrust Available

We can add this to our drag curve graph

Thrust Available Chart 1

Thrust Available

We could then measure the difference between

Thrust Available and Total Drag at different airspeeds

Thrust Available Chart 1

Thrust Available - Total Drag

For example
  • At 55 knots, with 770 lb of Thrust Available and 400 lb of Total Drag, the difference is 370 lb
  • At 90 knots, with 610 lb of Thrust Available and 280 lb of Total Drag, the difference is 330 lb

Thrust Available Chart 2

Thrust Available - Total Drag

Find the airspeed at which the difference between Thrust Available and Total Drag

is at its maximum

Thrust Available Chart 3

Thrust Available - Total Drag

  • For this particular aircraft, at 70 knots, Thrust Available is 700 lb and Total Drag is 290 lb
  • The leaves a difference between the two of 410 lb
  • There is no other airspeed where this difference is greater than 410 lb — the maximum excess thrust

Thrust Available Chart 4

Thrust Available - Total Drag

This airspeed is the best angle of climb speed, Vx

Thrust Available Chart 4

Best Angle of Climb Speed, Vx

In summary, the best angle of climb speed for an aircraft, is determined by the

maximum difference between Thrust Available and Total Drag

the maximum excess thrust

Power

What is power?
  • Power is defined as work performed over time
  • To determine power, we multiply work by time
  • In our case, work is thrust and time is airspeed
  • Therefore, Power = Thrust x Airspeed

Power

Power Required
  • Going back to our drag curve…
  • We know that in Straight and Level flight, Thrust = Drag
  • Therefore, we can view the Total Drag curve also as Thrust Required
  • We can then find out our Power Required by multiplying Thrust Required by Airspeed

Drag Curve 3

Power

Power Required, For example
  • At 60 knots airspeed, we require 350 lb of thrust to overcome drag
  • Or, we have a power required of 60 x 350 = 21000 knot/lb-1
  • At 120 knots airspeed, we required 480 lb of thrust to overcome drag
  • Or, we have a power required of 120 x 480 = 57600knot/lb-1

Drag Curve 5

Power

Power Required
  • To convert these units to horsepower (hp), we multiply by 0.003
  • 21000 x 0.003 = 63 hp — therefore, at 60 knots, the power required is 63 hp
  • 57600 x 0.003 = 172.8 hp — therefore, at 120 knots, the power required is 172.8 hp

Drag Curve 5

Power

Power Required
  • We can plot the Power Required against the Airspeed
  • We end up with a curve that looks like this — the Power Required Curve

Power Required Curve 1

Power

Power Available
  • Similarly, we can use our Thrust Available to determine our Power Available
  • Power Available = Thrust Available multiplied by Airspeed

Thrust Available Chart 1

Power

Power Available

We can add Power Available against Airspeed to our power curve

Power Available Curve 1

Power

Power Available - Power Required
  • We then find the maximum difference between our Power Available and Power Required
  • We find the Airspeed at that maximum to be 78 knots

Power Available Curve 2

Power Available - Power Required

This airspeed is the best rate of climb speed, Vy

Power Available Curve 2

Best Rate of Climb Speed, Vy

In summary, the best rate of climb speed for an aircraft, is determined by the

maximum difference between Power Available and Power Drag

the maximum excess power

Conclusion

  1. Total Drag is the sum of Induced and Parasite Drag
  2. Climb is caused by excess thrust
  3. Thrust Required is equivalent to Total Drag
  4. Thrust Available decreases as airspeed increases
  5. Best angle of climb speed (Vx) is the airspeed at the maximum amount of excess thrust
  6. Power = Thrust x Airspeed
  7. Power Required = Thrust Required x Airspeed
  8. Power Available = Thrust Available x Airspeed
  9. Best rate of climb speed (Vy) is the airspeed at the maximum amount of excess power