Lesson 3 · 40 min
Payload, Range and the Payload–Range Diagram
An aircraft does not have "a range". It can fly a full load a certain distance, trade some load for fuel to go farther, and fly farthest of all empty. The payload–range diagram shows the whole trade on one chart. It is the first thing an airline asks to see, and building it needs only the weights and Module 1's Breguet equation.
Learning objectives
- Define payload and the weights operators use (OEW, ZFW, MZFW, MTOW, MLW, fuel capacity) and relate them to the takeoff-weight build-up.
- Compute payload from passengers and baggage with standard masses.
- Construct a payload–range diagram from the weights and the Breguet equation, and explain what limits each segment.
- Find the payload that can be carried over a given range, and the range for a given payload.
Payload and the operator's weights
Sizing builds the takeoff weight as \(\Wo = W_{\text{crew}} + W_{\text{payload}} + \Wf + \We\). An airline uses a different set of names for the same idea, and the two are worth connecting:
| Weight | What it includes | In sizing terms |
|---|---|---|
| Empty weight | Structure, engines, landing gear, systems, fixed equipment (the manufacturer's empty weight) | \(\We\), approximately |
| Operating empty weight (OEW) | Empty weight plus crew, catering, water, unusable fuel and oil: everything needed to operate, except payload and usable fuel | \(\We + W_{\text{crew}}\) |
| Zero-fuel weight (ZFW) | OEW plus payload. Its maximum, MZFW, is a structural limit: fuel in the wing relieves wing bending, so the heaviest load without fuel is limited | \(\Wo - \Wf\) |
| Takeoff weight (TOW) | ZFW plus fuel. Its maximum, MTOW, is the design gross weight | \(\Wo\) at MTOW |
| Landing weight | TOW less the fuel burned. Its maximum, MLW, is set by the landing gear and structure | \(W_x\), the end of the mission |
| Fuel capacity | The usable fuel the tanks can hold, by volume times density (jet fuel is about \(0.8\ \text{kg/L}\)) | The largest possible \(\Wf\) |
Payload is what the customer pays to carry: passengers, their baggage and cargo for an airliner; the weapons, sensors or cargo of a military aircraft. Crew is not payload. For passengers, designers and operators use standard masses. This module uses \(100\ \text{kg}\) per passenger with baggage and \(90\ \text{kg}\) per crew member, round values typical of initial sizing; regulators publish their own (for example, European rules use \(84\ \text{kg}\) for an adult, including hand baggage, plus a standard mass for checked bags).
Building the payload–range diagram
Fix the aircraft (OEW, MTOW, maximum payload, fuel capacity) and its cruise (\(V\), \(C\), \(L/D\)). Hold back a reserve of fuel \(W_{\text{res}}\) that is never planned to be burned (Lesson 6). Then, for any takeoff weight and payload, every kilogram of fuel above the reserve is burned in a Breguet cruise from the takeoff weight down to the landing weight, \(\text{OEW} + \text{payload} + W_{\text{res}}\):
Range for a payload \(P\) (Breguet, fixed reserve)
\[ R = \colV{\frac{V}{C}}\,\colL{\frac{L}{D}}\,\ln\frac{\text{TOW}}{\text{OEW} + P + W_{\text{res}}}, \qquad \text{TOW} = \min\bigl(\text{MTOW},\ \text{OEW} + P + W_{\text{fuel,max}}\bigr) \]A simplified model: it treats the whole flight as cruise. Real diagrams add the fuel for taxi, takeoff, climb and descent (Lesson 5) and use detailed performance data, but they have exactly the same shape.
Three corner points define the diagram:
A: maximum payload
Maximum payload at MTOW: the fuel is whatever is left, \(\text{MTOW} - \text{OEW} - P_{\max}\). From zero range up to A, the payload is limited by the structure (MZFW) and the line is flat.
B: full tanks at MTOW
Beyond A, every kilogram of payload left behind is a kilogram of fuel added, at constant MTOW, until the tanks are full: \(P_B = \text{MTOW} - \text{OEW} - W_{\text{fuel,max}}\).
C: ferry range
Beyond B, the tanks are full, so the only way to go farther is to carry less: the aircraft takes off lighter than MTOW. With no payload at all, it reaches the ferry range.
Example 3.1 — The diagram of a narrow-body twin
An illustrative 150-seat twin has \(\text{OEW} = 42\,000\ \text{kg}\) (including crew), \(\text{MTOW} = 78\,000\ \text{kg}\), a maximum payload of \(19\,000\ \text{kg}\) and a fuel capacity of \(20\,000\ \text{kg}\). It cruises at \(830\ \text{km/h}\) with \(C = 0.58/\text{h}\) and an effective \(L/D = 16.5\), and keeps \(2600\ \text{kg}\) of reserve fuel. Find the corner points A, B and C.
Show solution
The range factor is \((V/C)(L/D) = (830/0.58)(16.5) = 23\,610\ \text{km}\).
A: TOW = MTOW = 78 000 kg; fuel \(= 78\,000 - 42\,000 - 19\,000 = 17\,000\ \text{kg}\), which fits in the tanks. Landing weight \(42\,000 + 19\,000 + 2600 = 63\,600\ \text{kg}\).
\[ R_A = 23\,610\ln\frac{78\,000}{63\,600} = 23\,610(0.2041) = 4819\ \text{km} \]B: full tanks at MTOW leave \(P_B = 78\,000 - 42\,000 - 20\,000 = 16\,000\ \text{kg}\); landing weight \(60\,600\ \text{kg}\).
\[ R_B = 23\,610\ln\frac{78\,000}{60\,600} = 5960\ \text{km} \]C: no payload, full tanks: TOW \(= 62\,000\ \text{kg}\), landing weight \(44\,600\ \text{kg}\).
\[ R_C = 23\,610\ln\frac{62\,000}{44\,600} = 7778\ \text{km} \]The design point
The requirement "150 passengers over 5000 km" is one point on this chart: the design payload at the design range. The design payload is usually less than the maximum payload, since a full cabin of passengers with their bags weighs less than the structure can carry; the difference is space for cargo on shorter flights. For the aircraft to meet the requirement, the design point must lie on or below its payload–range line.
Example 3.2 — Full cabin, and the longest flight
For the aircraft of Example 3.1: (a) How far can it carry a full cabin of 150 passengers at \(100\ \text{kg}\) each? (b) On a \(5500\ \text{km}\) route, how much payload can it carry?
Show solution
(a) \(P = 150(100) = 15\,000\ \text{kg}\), which is less than \(P_B = 16\,000\ \text{kg}\): the point lies between B and C, so the tanks are full and the aircraft takes off below MTOW.
\[ \text{TOW} = 42\,000 + 15\,000 + 20\,000 = 77\,000\ \text{kg} \] \[ R = 23\,610\ln\frac{77\,000}{42\,000 + 15\,000 + 2600} = 6048\ \text{km} \](b) \(5500\ \text{km}\) lies between A (4819) and B (5960): takeoff at MTOW, and the landing weight follows from Breguet:
\[ W_{\text{land}} = 78\,000\,e^{-5500/23\,610} = 61\,790\ \text{kg}, \qquad P = 61\,790 - 42\,000 - 2600 = 17\,190\ \text{kg} \]That is 150 passengers (15 000 kg) plus about 2.2 t of cargo.
What moves the diagram
- A better range factor \((V/C)(L/D)\) (new engines, a better wing) stretches the whole diagram to the right in proportion.
- A higher MTOW (a stronger structure, often a later version of the type) moves A and B to the right: more fuel at the same payload.
- More fuel capacity (an extra tank) moves B down and to the right and extends the ferry range, but helps only where the tanks were the limit.
- A lighter OEW helps everywhere: every kilogram saved is a kilogram of payload or fuel.
Families of aircraft are planned on this chart: a stretched version trades range for payload, a long-range version adds MTOW and tanks. Lesson 7 shows how much a kilogram of OEW, or a kilometre of range, costs in takeoff weight.
Check your understanding
Key takeaways
- OEW = empty weight + crew and operating items; ZFW = OEW + payload (limited by MZFW); TOW = ZFW + fuel (limited by MTOW and by tank capacity).
- Payload–range: flat at maximum payload to A; trade payload for fuel at MTOW to B (full tanks); then fly lighter to the ferry range C.
- With Breguet and a fixed reserve: \(R = (V/C)(L/D)\ln[\text{TOW}/(\text{OEW} + P + W_{\text{res}})]\).
- The design payload at the design range must lie on or below the line.
- Next, Lesson 4 adds the requirements that come from the airworthiness rules.