Module 4/5 · Weeks 10–12 · 30 h

Energy, power and endurance

DRT 112 Applied Physics for Aircraft Technology

About 85 minDraft, awaiting reviewLast updated 26 September 2026

By the end of this module you will be able to

Calculate work, kinetic energy, potential energy and power in flight situations
Explain the efficiency chain from battery to thrust and estimate the electrical power needed
Assess the effect of payload on power and flight time
Explain C-rating, internal resistance, voltage sag and heating in batteries
Apply heat and temperature concepts to safe battery use

Prerequisites: DRT 111 Module 1 (energy units) and DRT 112 Module 3 (induced power)

Energy limits every mission

In the field, the questions drone users ask most are “how long can it fly?” and “if I add equipment, how much shorter will the flight be?” DRT 111 showed a simple flight-time estimate from battery energy and average power. This module explains where that power comes from, where it is lost, and why weight affects flight time more than you might expect.

Work, energy and power

Work is force times distance moved in the direction of the force, $W_{work} = F d$ , measured in joules (J). Two kinds of energy are common in drone work:

E_{k} = \frac{1}{2} m v^{2} E_{p} = m g h

Power is the rate of using or converting energy, $P = E / t$ , in watts. When a constant force moves something at constant speed, $P = F v$ .

Example 1. Are these energies large or small?

A 2 kg drone flies at 15 m/s at a height of 100 m.

Kinetic energy $\frac{1}{2} (2) (1 5^{2}) = 225$ J
Potential energy $2 \times 9.81 \times 100 = 1962$ J, about 0.55 Wh

A 74 Wh battery holds about 135 times this potential energy. Almost all of a multirotor’s energy therefore goes not into height or speed but into pushing air down to stay aloft throughout the flight.

The efficiency chain

Battery energy passes through several stages before it becomes thrust, and each stage loses some as heat.

Battery energy passes through the ESC at 0.95, motor at 0.85 and propeller with figure of merit 0.65 to become thrust; overall efficiency about 0.52 — Figure 1. Energy conversion chain and approximate efficiencies

Overall efficiency is the product of the stage efficiencies:

η = η_{ESC} η_{motor} FM \approx 0.95 \times 0.85 \times 0.65 \approx 0.52

These are approximate values for a typical small drone; real values depend on the equipment and operating point and should be measured, as in the Module 3 lab. The electrical power required is

P_{elec} = \frac{P _{i}}{η}

Example 2. Hover and climb power

From Module 3, a 2 kg drone needs 123 W of ideal induced power.

Electrical hover power $123/0.52 \approx 237$ W
Climbing at 2 m/s needs extra mechanical power $m g v = 2 \times 9.81 \times 2 = 39.2$ W, or $39.2/0.52 \approx 75$ W more electrical power

These figures agree with the 300 W average used in DRT 111, which includes manoeuvring and other losses.

Payload and flight time

From Module 3, hover power scales as $P \propto T^{3/2}$ , and in hover $T = m g$ , so

P \propto m^{3/2}

Example 3. Adding 20% mass

Extra equipment raises total mass by 20%.

Power rises to $1. 2^{3/2} \approx 1.31$ times
Flight time on the same battery falls to $1/1.31 \approx 0.76$ , about 24% shorter

Mass rises 20% but flight time drops by more. That is why designers fight for every gram, and why a bigger battery does not always add flight time in proportion.

Batteries: current, resistance and heat

C-rating

The C-rating gives the maximum continuous discharge current relative to capacity:

I_{m a x} = C \times Q_{Ah}

A 5 Ah 25C battery is labelled for $25 \times 5 = 125$ A continuous. In practice, label ratings are often optimistic, so leave a margin.

Internal resistance and voltage sag

Every battery has internal resistance $R_{int}$ . At high current the terminal voltage sags and heat is generated inside:

Δ V = I R_{int} P_{loss} = I^{2} R_{int}

Example 4. Heat in a battery

A battery with 0.02 Ω total internal resistance supplies 20 A.

Voltage sag $20 \times 0.02 = 0.4$ V
Heat $2 0^{2} \times 0.02 = 8$ W
A 10-minute flight generates $8 \times 600 = 4800$ J. For a 0.5 kg battery with a specific heat of about 1000 J/(kg·K), ignoring cooling, the temperature rises by about $Δ T = Q / (m c) = 4800/ (0.5 \times 1000) \approx 9.6$ K

Internal resistance rises when a battery is very cold or ageing, so voltage sags more under load. The autopilot may then think the battery is nearly empty and return home earlier than necessary.

Lithium battery safety

Never charge or fly a battery that is swollen, dented or unusually hot.
Charge in a fire-safe container, supervised, with the charger set to the correct cell count.
Do not leave batteries in a car in the sun; Thailand’s heat speeds up ageing and raises fire risk.
For long-term storage, keep cells at about 3.8 V each, as makers recommend.

Module lab

In class

Using the thrust and power data from the Module 3 lab, find the gf/W efficiency at a thrust of one quarter of the example drone’s weight.
Estimate the example drone’s hover power and flight time, then compare with a real flight log or the maker’s figure.
Repeat for payload increases of 10%, 20% and 30%, and plot flight time against mass.

Common mistakes

Watch out

Assuming hover power is proportional to mass. It scales as $m^{3/2}$ .
Ignoring the efficiency chain. Real electrical power is almost double the ideal power.
Trusting C-ratings on the label completely. Leave a margin.
Forgetting heat. High current heats batteries and motors and shortens their life.

Summary

Work $F d$ , kinetic energy $\frac{1}{2} m v^{2}$ , potential energy $m g h$ , and power $P = E / t = F v$ .
A multirotor spends almost all its energy staying aloft, not storing potential energy.
Overall efficiency is the product of ESC, motor and propeller efficiencies, often about one half.
Hover power scales as $m^{3/2}$ : 20% more mass cuts flight time by about 24%.
C-rating limits current; internal resistance causes voltage sag and $I^{2} R$ heating.

Check your understanding

A 1.5 kg drone climbs 50 m. How much potential energy does it gain?
With ESC 0.94, motor 0.82 and FM 0.6, what is the overall efficiency?
Ideal power is 90 W and overall efficiency 0.5. What electrical power is needed?
If mass falls by 10%, by roughly what percentage does flight time rise?
What maximum continuous current is a 6 Ah 30C battery labelled for?

Answers

$1.5 \times 9.81 \times 50 \approx 736$ J
$0.94 \times 0.82 \times 0.6 \approx 0.46$
$90/0.5 = 180$ W
$0. 9^{- 3/2} \approx 1.171$ , about 17% longer
$30 \times 6 = 180$ A

Key formulas

Work	$W_{work} = F d$
Kinetic and potential energy	$E_{k} = \frac{1}{2} m v^{2}, E_{p} = m g h$
Power	$P = \frac{E}{t} = F v$
Overall efficiency	$η = η_{ESC} η_{motor} FM$
Electrical hover power	$P_{elec} = \frac{P _{i}}{η}$
Effect of mass on hover power	$P \propto m^{3/2}$
Maximum current from C-rating	$I_{m a x} = C \times Q_{Ah}$
Battery heating	$P_{loss} = I^{2} R_{int}, Q = m c Δ T$

Key references

Serway, R. A., & Jewett, J. W. (2018). Physics for scientists and engineers (10th ed.). Cengage.
Leishman, J. G. (2006). Principles of helicopter aerodynamics (2nd ed.). Cambridge University Press.
Quan, Q. (2017). Introduction to multicopter design and control. Springer.
Boylestad, R. L., & Nashelsky, L. (2013). Electronic devices and circuit theory (11th ed.). Pearson.

In class / field

Lab or field practice from worksheets with a safety checklist

Learning evidence: Checked worksheets and quiz results

Module quiz

This is a formative self-check, not a graded exam

Knowledge domain: Mathematics, physics and statistics · Electrical, electronics and power systems · Automation, robotics and swarms · Aircraft, structures and design

Energy, power and endurance

By the end of this module you will be able to

Energy limits every mission

Work, energy and power

The efficiency chain

Payload and flight time

Batteries: current, resistance and heat

C-rating

Internal resistance and voltage sag

Module lab

Common mistakes

Summary

Check your understanding

Key formulas

Key references

Further reading

Energy, power and heat in aircraft systems

Payload mass, centre of gravity and energy

In class / field

Module quiz

Energy, power and endurance

Lesson

By the end of this module you will be able to

Energy limits every mission

Work, energy and power

The efficiency chain

Payload and flight time

Batteries: current, resistance and heat

C-rating

Internal resistance and voltage sag

Module lab

Common mistakes

Summary

Check your understanding

Key formulas

Key references

Further reading

Energy, power and heat in aircraft systems

Payload mass, centre of gravity and energy

In class / field

Module quiz