Library / Flight dynamics and control / FLT-03
Flight dynamics and control
Specific total energy and energy height
Mechanical energy per unit mass of an aircraft: potential plus kinetic.
- Ref
- FLT-03
- Rev
- v1
- Field
- Flight dynamics and control
- Result
- eT [kJ/kg]
The specific total mechanical energy of an aircraft is the sum of its potential energy gh and kinetic energy Va²/2, each per kilogram. Dividing by g gives the energy height he = h + Va²/(2g), the altitude the aircraft could reach if all its speed were traded for height without loss. The result here is in kJ/kg for convenience; the formula is in J/kg.
Mechanical energy per unit mass of an aircraft: potential plus kinetic. Dividing by g gives the energy height, the altitude it would reach if all its speed were traded for height.
Calculator
- Energy height, eT/g1,183 m
- Potential part, g h9.81 kJ/kg
- Kinetic part, Va²/21.8 kJ/kg
- Kinetic share of the total15.5 %
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- At 1,000 m and 60 m/s the energy height is 1,183.5 m. The speed is worth 183.5 m of altitude, so, ignoring drag, trading it for height would raise the aircraft by that much.
- Speed dominates at high speed and low altitude. At 200 m/s the kinetic part is 20 kJ/kg, against 9.81 kJ/kg of potential energy at 1,000 m.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (kJ/kg) | Local step | Change in result |
|---|---|---|---|---|---|---|
| h Altitude | 0 to 10,000 m | 1.8 | 99.9 | 98.1 | +10% | +8.45 % |
| Va Airspeed | 20 to 300 m/s | 10.01 | 54.81 | 44.8 | +10% | +3.26 % |
Sweep of Airspeed
| Airspeed (m/s) | Specific total energy (kJ/kg) |
|---|---|
| 20 | 10.01 |
| 55 | 11.32 |
| 90 | 13.86 |
| 125 | 17.62 |
| 160 | 22.61 |
| 195 | 28.82 |
| 230 | 36.26 |
| 265 | 44.92 |
| 300 | 54.81 |
Sweep one variable
Variables and how each one contributes
Specific total energy
What the equation gives you. Everything else feeds it.
Altitude
The altitude in m. Potential energy is directly proportional to altitude, so the total energy rises with it, less than proportionally when speed contributes too. Raising it by 10 % (to 1,100) moves the result by +8.45 %, from 11.61 to 12.59 kJ/kg.
Airspeed
The airspeed in m/s. Kinetic energy grows with the square of speed, so the total rises by more than the percentage increase in speed. Raising it by 10 % (to 66) moves the result by +3.26 %, from 11.61 to 11.99 kJ/kg.
Worked example with the values above
- Potential energy: g h = 9.81 × 1,000 = 9,810 J/kg.
- Kinetic energy: ½Va² = 0.5 × 60² = 1,800 J/kg.
- eT = 9,810 + 1,800 = 11,610 J/kg = 11.61 kJ/kg.
Assumptions and limits
- Constant gravity g = 9.81 m/s² and a flat, non-rotating Earth over the heights concerned.
- Airspeed taken as the speed that carries kinetic energy; wind and aircraft energy sources are not included.
Common mistakes
- Using indicated airspeed instead of true airspeed. Kinetic energy depends on the true speed through the air mass.
- Forgetting the energy is per unit mass. Multiply by the aircraft mass to get joules.
Statistics and uncertainty
Airspeed enters squared, so a 2 % error in Va is a 4 % error in the kinetic term. With the kinetic share at 15.5 %, that is 0.62 % of the total here, but at high speed it dominates. Altitude errors enter directly, so a barometric altitude that is out by 30 m changes the potential term by 0.294 kJ/kg.
Where it is used
- Energy-based flight control, where height and speed are managed together.
- Estimating how much altitude can be gained by trading speed, or the zoom climb height available.
Maths you need
- Potential and kinetic energy: g h and ½ V²
- Specific quantity: a quantity per unit mass