# How are thrust specifications for multi-nozzle engines given?

The Soviet R-7 ICBM used 5 RD-107/RD-108 engines in its first stage in a "Quincunx" formation. Each engine had four CD nozzles, and 1 propellant pump, common for all four nozzles. The thrust of the engine is given as 1000/1020 kN at sea level. Is this thrust the cumulative thrust from all 4 nozzles, or from each individual nozzle?

• asparagusing intensifies May 7 at 16:10

Instead of seeking sources, I'll do a little bit of calculation:

1000kN per engine:

1000kN is about 100 tons-force. Wikipedia lists R7 launch mass as 280 tons. 500 tons-force of thrust (5 engines x 100 tons) applied to 280 tons of weight gives a sane, reasonable initial thrust-to-weight ratio of 1.7 which is a rather brisk, healthy pace of climb for an orbital or ballistic rocket. (compare: Falcon 9: 1.28, Soyuz: 1.4-1.6, Saturn V: 1.15, Vostok - 1.65)

1000kN per nozzle:

2000 tons-force (4 nozzles x 5 engines x 100 tons thrust) applied to the same 280 tons weight would result in launch TWR of 7.1 which is not sane. It's something expectable from interceptor missiles, not ICBMs. Japanese SS-520-5 aka Lambda 4S (with its 26kg payload capacity) comes close, but I don't know anything powered with liquid engines capable of that much TWR, never mind it's completely unreasonable and pointless unless you need to hit an ICBM that is already coming down.

Concluding: The number is given relative to engine, otherwise the majestic R7 would be zipping like an interceptor.

• You beat me to it. I worked out either about $5\,\mathrm{ms^{-2}}$ (sane) or about $40\,\mathrm{ms^{-2}}$ (not sane).
– user21103
May 6 at 13:49
• At sea level, the thrust is 810kN for the RD-107, so the ignition TWR is around 1.5. May 6 at 14:41
• @SF. I am not seeking any exact values or intend to get into any kind of calculations. I read about single chamber engines and also about multiple chamber engines. So I was curious to know if the thrust values are cumulative of all four chambers/nozzles, or they were individual to each. In this context I request you to read my comments on Russel's answer. In view of the limit on characters, I had to split my views in multiple comments. Please bear with me for that. May 6 at 18:30
• @SF. While I had no problem following your calculations, your conclusion is stated more clearly in your last comment than in the answer. That might make the difference to the OP if they weren't expecting numbers May 7 at 13:55

The nozzle is not the engine.

Each nozzle is attached to one combustion chamber, but by convention, a complex of multiple combustion chambers sharing a single turbopump, such as the RD-107/RD-108, is referred to as a single engine.

Thus the thrust figure given is for all four combustion chambers, that is, the engine as a whole. SF's sanity check confirms this.

Note that the thrust figures you give in your question are for the RD-107 and RD-107A at high altitude; at sea level the thrust for the original (R-7) RD-107 is 810kN.

• To the extent I have read, the converging part of a CD nozzle, is attached to the combustion chamber so much so that its practically "one piece". As a result, combustion chamber, together with CD nozzle is the "thrust generator". Each combination with its own turbopump is generally considered as "one engine". In some cases, two such "thrust generators"- in this case four such thrust generators had one common turbo pump, and hence this complete assembly (1 turbopump with 4 chambers & CD nozzles) was considered as one engine. - to be continued in next comment. May 6 at 18:05
• ...Continued from previous comment: Thrust is generated when propellants burn in combustion chamber, and exhaust takes place thro D nozzle. So amount of thrust generated by each chamber-nozzle combination will depend on the quantity of mass burned, which in turn will depend on the amount of mass fed. With only one pump to feed the propellant, unless the flow distribution is practically exactly same for all 4 chambers, the thrust generated by them would vary. So, my question can also be worded as: To be continued in next comment... May 6 at 18:11
• The thrust value mentioned on the web page (it not important if it is at SL or Vac), is the one which would be available by burning of the total quantity of propellants supplied to all four chambers collectively, or it is the value generated by each chamber, by burning the amount of propellants received by that chamber... To be continued in next comment... May 6 at 18:20
• By convention, multiple combustion chambers sharing a single turbopump are referred to as a single engine. May 6 at 20:11
• @Niranjan Additionally, higher thrust results from higher chamber pressure which must be overcome by pressure of fuel and oxidizer produced by the turbopump, to be injected into the combustion chamber. So the multi-chamber system is self-balancing as increase of pressure in one chamber will cause more of the propellants to flow towards chambers with lower pressure (which in order, increases pressure and thrust there).
– SF.
May 6 at 23:10