Private Pilot

The other Task F elements give you numbers. This one explains why the numbers behave the way they do. Performance is aerodynamics with a throttle and a runway attached. The same four forces and the same angle of attack that govern every maneuver also set your takeoff roll, your climb, and your glide.

The air story from the density-altitude element (K2A) and the weight story from the loading element (K2B) both come together here in the same lift equation. That turns the chart values from K1 into cause and effect.

Every performance number comes back to two things: how hard the wing is working (angle of attack) and what that work costs (drag). Understand those two and the takeoff roll, the climb, and the glide stop being mysteries.

The four forces

The four forces are lift, weight, thrust, and drag. In steady, unaccelerated flight they balance in two pairs: lift against weight, and thrust against drag. Upset the balance and the airplane accelerates somewhere:

• More thrust than drag, and the airplane speeds up (or, with the nose raised, climbs).
• More lift than weight, and the flight path curves upward. Lift exceeds weight only momentarily, to start the climb; once the climb is steady, lift is a little less than weight and the airplane climbs on the thrust surplus.
• Less of either, and it slows or descends.

Every phase of flight is just a different imbalance of the same four forces:

• Takeoff is a deliberate surplus of thrust over drag, to accelerate.
• Climb is sustained by that same thrust surplus. Lift momentarily exceeds weight to start the climb; once the climb is steady, lift is slightly less than weight (L = W cos γ) and part of the excess thrust acts upward along the inclined flight path. Excess thrust, not excess lift, is what gains you altitude.
• Descent is weight winning. Drag exceeds thrust, and the along-path component of weight makes up the difference. Gravity does the work along the flight path, which is why descents come "for free."
• Cruise is all four forces back in balance.

The diagram below cycles through the four standard states. Watch the four vectors change size. Climbing and descending teach the most.

Interactive

Aerodynamics · PA.I.F.K3

The four forces

Forces balanced — steady level

toggle the flight state to watch the four vectors resize.

Flight state

Steady levelClimbingDescendingAccelerating

Vertical balance L = W, horizontal balance T = D. The pairs are equal length, so there is no net force — constant altitude, constant airspeed.

Every phase of flight is just a particular imbalance of the same four vectors — L, W, T, and D. Magnitudes are illustrative, not POH values. In a steady climb or descent the small lift-weight gap is the cos γ effect of the inclined flight path; the airplane is drawn level for clarity.