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Thrust and weight

Rockets and landing · level 3, lesson 2 of 6

A question to start

The Saturn V weighed about 29,000 kN on the launch pad, and its engines pushed with about 34,000 kN. How much push was left over to lift it?

The idea

Two forces act on a rocket at lift-off:

  • its weight, pulling down;
  • its thrust, pushing up.

Take one from the other to find the net force, the push that is left over:

\[\text{net force} = \text{thrust} - \text{weight}.\]
  • If the net force is positive (thrust bigger), the rocket speeds up upwards.
  • If it is zero, the rocket hovers, or keeps going at a steady speed.
  • If it is negative (weight bigger), the rocket cannot lift off.
stays downhoversrisesgreen: thrust · red: weight

The thrust-to-weight ratio compares them: thrust divided by weight. A rocket needs more than 1 to lift off. Big rockets launch at about 1.2 to 1.5: enough to rise, but not so much that they need huge engines. A rocket on Mars, where the weight is only 38% as much, could lift off with much smaller engines.

Worked examples

1. Saturn V. \(34{,}000 - 29{,}000 = 5{,}000\) kN net, upwards. Thrust-to-weight ratio: \(34{,}000 \div 29{,}000 \approx 1.2\).

2. A model rocket. Mass 0.1 kg, so weight about 1 N. Its motor gives 6 N. Net force \(6 - 1 = 5\) N up, and the thrust-to-weight ratio is 6: it leaps off the pad.

3. The same rocket on Mars. A rocket weighing 1,000 kN on Earth weighs only 380 kN on Mars. Engines of 500 kN would not lift it on Earth, but on Mars the net force is \(500 - 380 = 120\) kN up.

Try it

  1. A rocket weighs 500 kN and its engines push 600 kN. Find the net force. Will it lift off?
  2. A rocket weighs 800 kN and its engines push 750 kN. What happens?
  3. Find the thrust-to-weight ratio of a rocket with 1,200 kN of thrust and 1,000 kN of weight.
  4. A lander hovers above Mars. Its weight there is 4,000 N. What is its thrust?
Answers
  1. \(600 - 500 = 100\) kN up. Yes.
  2. The weight is bigger, so it stays on the pad.
  3. \(1{,}200 \div 1{,}000 = 1.2\).
  4. 4,000 N: to hover, thrust equals weight.

Common mistake

"The rocket lifts off as soon as the engines start." The engines must first push harder than the whole weight. Big rockets are often held down by clamps for a few seconds while the engines build up to full thrust.

Where it leads