Calculating rocket engine thrust

[T-10a]

Hey there!

I'm trying to calculate the thrust of an NTR (to assist in Module Manager configuration of Atomic Age, Ven's Stock Revamp and Stock NTRs).

I've got the exhaust velocity (and therefore specific impulse) from here at Atomic Rockets. Issue is, I'm stuck on how to get thrust.

I know the formula (F = mDot *Ve), I'm just stuck on trying to find mDot. For reference, here's the NTR specs I have so far:

Exhaust velocity: 6358 m.s.-1 (649s specific impulse)

Chamber temp: 2000 deg. Kelvin

Propellant: Hydrogen (1.41 heat  ratio, molar mass of 2.)

Pressure: 68 atm (chamber), 1 atm (exhaust)

[bigcalm]

You're missing how fast the fuel is burnt essentially.

F = ma = momentum / time = (mass of fuel ejected * velocity of fuel ejected) / time = \frac{ m_{fuel} * v_e } { t }

(NB.  This is what m dot means, ultimately the derivative of mass by time, dm/dt ).  So you'll need to find out how much fuel per unit time is being consumed in order to calculate thrust.

Consider an ion engine - it ejects a very small percentage of its mass per second - giving it very low thrust, but because v_e is very high, it gives extraordinary efficiency - very high delta v.

Compare that to say a mainsail engine, it's ejecting a huge amount of fuel per second, giving it very high thrust, but it's not hugely efficient because v_e is much, much lower.

 

[GoSlash27]

T-10a,
 As bigcalm pointed out, you need m-dot to figure out the thrust. You need to know how big the engine is; how quickly you can stuff fuel down it's throat. Since the engine can theoretically be any size, there is no single answer.

Best,
-Slashy

[Bill Phil]

Hmm... This won't really be something you calculate. Chamber pressure and throat area may help, but really, these are numbers you'd have to just make up given these circumstances. Looks like it may an atmosphere optimized LANTR (in which case, you'd want the exit pressure to be below 1 atmosphere, as you quickly lose atmospheric pressure when launching). It appears that the stock NERVA has a mass flow rate (mdot) of about 7.66 kg. 

How big is this engine?

[PB666]

1 hour ago, Bill Phil said:

Hmm... This won't really be something you calculate. Chamber pressure and throat area may help, but really, these are numbers you'd have to just make up given these circumstances. Looks like it may an atmosphere optimized LANTR (in which case, you'd want the exit pressure to be below 1 atmosphere, as you quickly lose atmospheric pressure when launching). It appears that the stock NERVA has a mass flow rate (mdot) of about 7.66 kg. 

How big is this engine?

The formula is virtually useless since no NERVA runs at 5000K or 1H, and your really have no idea for any gas how many free radicals are in the exhaust stream

 If you want to shorten it is  Ve = 6188 SQRT (k/(k-1)* 1/M)) : the reason you want to shorten the equation is the Mole fraction of the exhaust changes its not exact (exept in the case of helium which is 100%) H is distributed between H₂ and H, H20 is distributed between H* and OH*. Remember these ions have just traveled through the overheated core of a nuclear reactor we expect alot of free radicals so the T also effect M for every molecule except Helium, Neon, Argon, Krypton and Xenon.
For H k = 1.41 M = 2
For He k = 1.66 M = 4
For water k = 1.30  M = 18 (which probably more like 10 but . .wikipedia- " When water is heated to well over 2000 °C, a small percentage of it will decompose into OH, monoatomic oxygen, monoatomic hydrogen, O₂, and H₂. " . )

So for H Ve = 8260
for He Ve = 4901
for water Ve = 3036 - 4000

You could use boron I suppose but as you can see the trend higher elemental mass is not good for ISP.

Now to the nitty gritty, well for short, ur f-d, at least if you want to throttle the engine realistically. The ISP is temperature dependent higher temperature means higher ISP. But the engine is damaged by high temperature, so the temperature is a function of heat flux, Some other gases of choice. CO2 is not  a gas of choice its M is 44 SQRT is 6.63 so about 1/3rd the ISP of helium. It decomposes at 3500K and 68 ATM to about 20% CO and O2. Neither of which really help CO is extremely stable. Methane at higher temperatures decomposes to 2H2  -  and C at 1073 k but carbon polymerizes and forms carbon tubes (not desired). However this can be prevented by discharging large amount of electons into the gas  at the chamber outlet. Methane can control temperature since is absorbs heat and turns it into chemical energy, giving a slightly better throttle range, but for the most part when you are running the engine you cannot throttle without slowing the reaction down and waiting for the heat to dissipate.

So I imagine that the way they run a nuclear engine is that the trigger the uranium, they wait for heat to climb, then open the throttles until temperature and mass flow equilibrate, before shutdown do the opposite, silence the uranium, wait then back off on fuel flow until its safe. In the equation on nuclear rockets T is preset, I'm sure that its not and since it is not it will be difficult to throttle, at least without some lag. I don't know but I can be pretty sure that throttling and controlling T are not the same as in a chemical rocket.

 

[PB666]

.

6 hours ago, T-10a said:

Hey there!

I'm trying to calculate the thrust of an NTR (to assist in Module Manager configuration of Atomic Age, Ven's Stock Revamp and Stock NTRs).

I've got the exhaust velocity (and therefore specific impulse) from here at Atomic Rockets. Issue is, I'm stuck on how to get thrust.

I know the formula (F = mDot *Ve), I'm just stuck on trying to find mDot. For reference, here's the NTR specs I have so far:

Exhaust velocity: 6358 m.s.-1 (649s specific impulse)

Chamber temp: 2000 deg. Kelvin

Propellant: Hydrogen (1.41 heat  ratio, molar mass of 2.)

Pressure: 68 atm (chamber), 1 atm (exhaust)

See below, your temperature is too low and you are wasting ISP, if you uped it to 3600 you could get 8200 ISP. You would also have a higher mole fraction of H* versus H at that temperature. If you discharged high amounts of electrons into the chaber outlet its potential that you could stabilize more H and get an even higher ISP. You could set the positive charge on the nozzle outlet. Theres a potential ISP of 10,000.

The specific question you ask Fuel flow * ISP * 9.806 = F    δm/δt = fuel flow in kg/sec.

[T-10a]

Thanks for all the replies. Keep in mind, I know a 2000K NTR is not ideal (as stated before, it's most likely the temperature range of an atmospheric LANTR).

7 hours ago, Bill Phil said:

Hmm... This won't really be something you calculate. Chamber pressure and throat area may help, but really, these are numbers you'd have to just make up given these circumstances. Looks like it may an atmosphere optimized LANTR (in which case, you'd want the exit pressure to be below 1 atmosphere, as you quickly lose atmospheric pressure when launching). It appears that the stock NERVA has a mass flow rate (mdot) of about 7.66 kg. 

How big is this engine?

I copied the temp from the comparison of specific impulse of the SSME (at about 4200K) to a 2000K NTR in the Atomic Rockets Engine page, near the section I linked to. Therefore, I do not know how big it will be. Also, how did you calculate the stock NERVA mDot? 

As a related question, when I see papers on untested engine designs (such as GCNR, fusion or antimatter engine designs), how would they get the thrust and mass flow of the engine? There seems to be no physical engine testing for such engines.

[PB666]

1 hour ago, T-10a said:

Thanks for all the replies. Keep in mind, I know a 2000K NTR is not ideal (as stated before, it's most likely the temperature range of an atmospheric LANTR).

I copied the temp from the comparison of specific impulse of the SSME (at about 4200K) to a 2000K NTR in the Atomic Rockets Engine page, near the section I linked to. Therefore, I do not know how big it will be. Also, how did you calculate the stock NERVA mDot? 

As a related question, when I see papers on untested engine designs (such as GCNR, fusion or antimatter engine designs), how would they get the thrust and mass flow of the engine? There seems to be no physical engine testing for such engines.

NERVA is not in the same thrust class of engine as SSME. The SSME is a two stage active turbocharged (as apposed to passive expansion cycle engines) cryogenic engine. If you dumped that much fuel on the Nuclear reactor it would go cold in seconds. If you had a reactor that had enough fuel to heat it it would go prompt critical in seconds. If you want to compare NERVA to something use the RL10b-2.

 

[T-10a]

Sorry, I misspoke where I got the comparison from. Here's the quote where I got the data from:

From the link in the OP:

Quote

As an example: the chemical engines on the Space Shuttle Main Engine (SSME) have a much higher temperature than a solid core nuclear thermal rocket (NTR) (4,000K as opposed to 2,000K). But the NTR has a higher exhaust velocity because it uses low molecular weight hydrogen as propellant, instead of that high molecular weight water that comes out of the SSME. So the NTR has a theoretical maximum exhaust velocity of around 8,000 m/s while the SSME is lucky to get 4,400 m/s. Behold the power of low molecular weight propellant: the higher temperature of the SSME is no match for the NTR's lower weight propellant.

Why cannot chemical engines use low molecular weight propellant? Because in chemical engines, the fuel and the propellant are one and the same, but in an NTR the fuel is the uranium and the propellant is whatever you want to use. With chemical you are stuck with whatever chemical reaction products are left over after the fuel has finished burning.

Though looking at it again, I can see why you think the comparison is a bad one.

Edited January 2, 2018 by T-10a

[PB666]

3 hours ago, T-10a said:

Sorry, I misspoke where I got the comparison from. Here's the quote where I got the data from:

From the link in the OP:

Though looking at it again, I can see why you think the comparison is a bad one.

SSME is pretty decent considering the bleed off for two the turbopumps system. Nuclear thermal rockets ISP in my opinion are poor considering the potential of fission.  NTRs IMO are barely worth the effort, I guess thats why NASA talking about building a cryogenic fuel station in EM orbit. And to be frank all you really need an RL10B-2 for if you have decent solar is to push it out of Earths orbit quickly and switch on some new age solar panels and ION drive.

They have a decent space engine RL10b-2, and once it is in space it performs well, it produces 4600 Ve and it weight 277 kg, The hydrogen issue is the same with NTR as with R10LB-2 so How much ISP are you willing to trade for 2T of rocket motor.
Not only that but RL10b-2 is in production and is actively being used.

[T-10a]

True. Doing the math for a liquid or gas-core NTR nets better ISPs (1486s for liquid, around 1700s for a closed GCNR), but development for those is about as near future as everyone claims sustainable fusion reactors are. Open-cycle is even more potent, but a radioactive spewing rocket engine is one hell of a PR killer for nasa. A benefit of a NTR is using one as bimodal generator may be useful, but strapping on photovoltaics to something like ACES could be just as useful in the near future.

Edited January 2, 2018 by T-10a

[PB666]

15 hours ago, T-10a said:

True. Doing the math for a liquid or gas-core NTR nets better ISPs (1486s for liquid, around 1700s for a closed GCNR), but development for those is about as near future as everyone claims sustainable fusion reactors are. Open-cycle is even more potent, but a radioactive spewing rocket engine is one hell of a PR killer for nasa. A benefit of a NTR is using one as bimodal generator may be useful, but strapping on photovoltaics to something like ACES could be just as useful in the near future.

To be quite honest if you are developing an NTR, NASA is a no-go to begin with, or at least not near future in its deployment. So you might want to build the rocket for a despotic demagogue somewhere who wants to do his wild thing on Mars.

The second thing is that the Uranium on NTRs is completely safe until fired, and if you are using this as a deep stage engine you are only going to want to fire it when you are well clear of Earth. Its better to have your late circularization engines to give you a apogee somewhere beyond GSO where you can fire it and no-one will really figure it out until months later. Although I must say USAF tracks every new object in space, particularly from despotic leadership countries.