BE-4 Reverse Engineered

[MikeM8891]

With the available data on the BE-4 sea level engine, I have reverse engineered some other likely performance numbers. The performance numbers are based on the published chamber pressure of 1950 psi (ArsTechnica.com), sea level thrust of 550,000 lb (BlueOrigin.com), and an estimated exit nozzle diameter of 72 in (+/- 3 in) from a rendering by Blue Origin (Twitter.com/blueorigin). I also attached some estimated thrust chamber dimensions based on the above data and an image of the thrust chamber (which is also attached). I included some uncertainties of the dimensions because some aspects of thrust chamber design are more art than engineering. Specifically, the thrust chamber upstream of the throat can be all sorts of proportions and my predicted chamber is surprisingly short and stout so I am pretty uncertain about its length.

Predicted BE-4 Sea Level Engine Performance

Property	Metric	Imperial	Uncertainty
Chamber Pressure	134 bar	1950 psi
Thrust at sea level	2,447 kN	550,000 lb
Thrust in vacuum	2,713 kN	609,924 lb	+/-0.8%
Specific Impusle at sea level	312 sec	312 sec	+/-1 sec
Specific Impusle in vacuum	346 sec	346 sec	+/-3 sec

Dimensional Uncertainty

Dimension	Uncertainty
Nozzle Exit Diameter	+/- 4.2%
Nozzle Throat Diameter	+/- 0.9%
Chamber Diameter	+/- 4.7%
Expansion Nozzle Length	+/- 5.5%
Chamber Length	+/- 32.6%

[HMXHMX]

With the available data on the BE-4 sea level engine, I have reverse engineered some other likely performance numbers. The performance numbers are based on the published chamber pressure of 1950 psi (ArsTechnica.com), sea level thrust of 550,000 lb (BlueOrigin.com), and an estimated exit nozzle diameter of 72 in (+/- 3 in) from a rendering by Blue Origin (Twitter.com/blueorigin). I also attached some estimated thrust chamber dimensions based on the above data and an image of the thrust chamber (which is also attached). I included some uncertainties of the dimensions because some aspects of thrust chamber design are more art than engineering. Specifically, the thrust chamber upstream of the throat can be all sorts of proportions and my predicted chamber is surprisingly short and stout so I am pretty uncertain about its length.

Predicted BE-4 Sea Level Engine Performance

Property	Metric	Imperial	Uncertainty
Chamber Pressure	134 bar	1950 psi
Thrust at sea level	2,447 kN	550,000 lb
Thrust in vacuum	2,713 kN	609,924 lb	+/-0.8%
Specific Impusle at sea level	320 sec	320 sec	+/-5 sec
Specific Impusle in vacuum	355 sec	355 sec	+/-3 sec

Dimensional Uncertainty

Dimension	Uncertainty
Nozzle Exit Diameter	+/- 4.2%
Nozzle Throat Diameter	+/- 0.9%
Chamber Diameter	+/- 4.7%
Expansion Nozzle Length	+/- 5.5%
Chamber Length	+/- 32.6%

Your analysis suggests a contraction ratio ~3.25 (exactly 3.247:1, so design point must be 3.25:1).  That's fairly high but consistent with trying to get very high combustion efficiency.  I tend to design between 3-4 typically.

[MikeM8891]

With the available data on the BE-4 sea level engine, I have reverse engineered some other likely performance numbers. The performance numbers are based on the published chamber pressure of 1950 psi (ArsTechnica.com), sea level thrust of 550,000 lb (BlueOrigin.com), and an estimated exit nozzle diameter of 72 in (+/- 3 in) from a rendering by Blue Origin (Twitter.com/blueorigin). I also attached some estimated thrust chamber dimensions based on the above data and an image of the thrust chamber (which is also attached). I included some uncertainties of the dimensions because some aspects of thrust chamber design are more art than engineering. Specifically, the thrust chamber upstream of the throat can be all sorts of proportions and my predicted chamber is surprisingly short and stout so I am pretty uncertain about its length.

Predicted BE-4 Sea Level Engine Performance

Property	Metric	Imperial	Uncertainty
Chamber Pressure	134 bar	1950 psi
Thrust at sea level	2,447 kN	550,000 lb
Thrust in vacuum	2,713 kN	609,924 lb	+/-0.8%
Specific Impusle at sea level	320 sec	320 sec	+/-5 sec
Specific Impusle in vacuum	355 sec	355 sec	+/-3 sec

Dimensional Uncertainty

Dimension	Uncertainty
Nozzle Exit Diameter	+/- 4.2%
Nozzle Throat Diameter	+/- 0.9%
Chamber Diameter	+/- 4.7%
Expansion Nozzle Length	+/- 5.5%
Chamber Length	+/- 32.6%

Your analysis suggests a contraction ratio ~3.25 (exactly 3.247:1, so design point must be 3.25:1).  That's fairly high but consistent with trying to get very high combustion efficiency.  I tend to design between 3-4 typically.

I agree the contraction ratio seems high. I have a textbook that suggests it should be around 1.8-2.7. There is actually a lot of uncertainty in my calculation. Based on the photo of the combustion chamber I get a contraction ratio of 3.0 but since this is based on the outer dimensions of the throat and chamber liner I believe the actual contraction ratio is higher. The the outer dimensions of the chamber based on the rendering posted to twitter is ~28.13 inches.  I figured this would be the largest the chamber could be since it is based on the outer dimension.  A 28.13-inch chamber results in a contraction ratio of ~3.55. So I figure the contraction ratio could be 3.0-3.5.

[MikeM8891]

To supplement my calculations, the throat diameter is based on solving for the vacuum thrust coefficient. The vacuum thrust coefficient can be calculated two ways: as a function of vacuum thrust, chamber pressure, and throat area; or as a function of pressure ratio, heat capacity ratio, and expansion ratio, where vac thrust = SL thrust + exit nozzle area x 1 atm. I set these functions equal to each other and solved for the unknowns. The max vacuum thrust coefficient and expansion ratio corresponds to the max exit nozzle area and min heat capacity ratio. From here the throat diameter is easily calculated from the expansion ratio and exit nozzle diameter.

Inputs	min	max	units
Exit Nozzle Area	2.41	2.85	sq m
Vacuum Thrust	2,691	2,735	kN
Chamber Pressure	134.4	134.4	bar
Heat Capacity Ratio	1.21	1.31
Outputs
Expansion Ratio	21.0	25.7
Vacuum Thrust Coefficient	1.742	1.835
Throat Diameter	0.376	0.383	m

[Rocket Surgeon]

With the available data on the BE-4 sea level engine, I have reverse engineered some other likely performance numbers. The performance numbers are based on the published chamber pressure of 1950 psi (ArsTechnica.com), sea level thrust of 550,000 lb (BlueOrigin.com), and an estimated exit nozzle diameter of 72 in (+/- 3 in) from a rendering by Blue Origin (Twitter.com/blueorigin). I also attached some estimated thrust chamber dimensions based on the above data and an image of the thrust chamber (which is also attached). I included some uncertainties of the dimensions because some aspects of thrust chamber design are more art than engineering. Specifically, the thrust chamber upstream of the throat can be all sorts of proportions and my predicted chamber is surprisingly short and stout so I am pretty uncertain about its length.

Predicted BE-4 Sea Level Engine Performance

Property	Metric	Imperial	Uncertainty
Chamber Pressure	134 bar	1950 psi
Thrust at sea level	2,447 kN	550,000 lb
Thrust in vacuum	2,713 kN	609,924 lb	+/-0.8%
Specific Impusle at sea level	320 sec	320 sec	+/-5 sec
Specific Impusle in vacuum	355 sec	355 sec	+/-3 sec

Dimensional Uncertainty

Dimension	Uncertainty
Nozzle Exit Diameter	+/- 4.2%
Nozzle Throat Diameter	+/- 0.9%
Chamber Diameter	+/- 4.7%
Expansion Nozzle Length	+/- 5.5%
Chamber Length	+/- 32.6%

This is fascinating, informative and very useful!
Which of the above variables could you realistically alter without having to completely redesign the engine to squeeze more performance out of it? see Merlin.

[MikeM8891]

This is fascinating, informative and very useful!
Which of the above variables could you realistically alter without having to completely redesign the engine to squeeze more performance out of it? see Merlin.

Raising the chamber pressure and enlarging the expansion nozzle would be the simplest way to increase both thrust and specific impulse.

[MikeM8891]

Predicted BE-4 Sea Level Engine Performance

Property	Metric	Imperial	Uncertainty
Chamber Pressure	134 bar	1950 psi
Thrust at sea level	2,447 kN	550,000 lb
Thrust in vacuum	2,713 kN	609,924 lb	+/-0.8%
Specific Impusle at sea level	320 sec	320 sec	+/-5 sec	316+/-9 sec
Specific Impusle in vacuum	355 sec	355 sec	+/-3 sec	351+/-7 sec

I am adjusting my specific impulse prediction because the prediction was based on analyzing the SpaceX Raptor performance, specifically the characteristic exhaust velocity (c*). Based on the published design performance of the Raptor, I expect c* to be between 1879-2015 m/s. However the Raptor is likely to have more efficient combustion than the BE-4 because both propellants are expected to enter the combustion chamber as gases.  Available data published in textbooks puts the c* of LOX/CH4 at 1838-1857 m/s.  This puts the expected lower end of the BE-4 Isp at 308 sec @ SL and 344 sec @ vac.

[Rocket Surgeon]

Predicted BE-4 Sea Level Engine Performance

Property	Metric	Imperial	Uncertainty
Chamber Pressure	134 bar	1950 psi
Thrust at sea level	2,447 kN	550,000 lb
Thrust in vacuum	2,713 kN	609,924 lb	+/-0.8%
Specific Impusle at sea level	320 sec	320 sec	+/-5 sec	316+/-9 sec
Specific Impusle in vacuum	355 sec	355 sec	+/-3 sec	351+/-7 sec

I am adjusting my specific impulse prediction because the prediction was based on analyzing the SpaceX Raptor performance, specifically the characteristic exhaust velocity (c*). Based on the published design performance of the Raptor, I expect c* to be between 1879-2015 m/s. However the Raptor is likely to have more efficient combustion than the BE-4 because both propellants are expected to enter the combustion chamber as gases.  Available data published in textbooks puts the c* of LOX/CH4 at 1838-1857 m/s.  This puts the expected lower end of the BE-4 Isp at 308 sec @ SL and 344 sec @ vac.

What text books are you using to help guide your analysis?

[MikeM8891]

Predicted BE-4 Sea Level Engine Performance

Property	Metric	Imperial	Uncertainty
Chamber Pressure	134 bar	1950 psi
Thrust at sea level	2,447 kN	550,000 lb
Thrust in vacuum	2,713 kN	609,924 lb	+/-0.8%
Specific Impusle at sea level	320 sec	320 sec	+/-5 sec	316+/-9 sec
Specific Impusle in vacuum	355 sec	355 sec	+/-3 sec	351+/-7 sec

I am adjusting my specific impulse prediction because the prediction was based on analyzing the SpaceX Raptor performance, specifically the characteristic exhaust velocity (c*). Based on the published design performance of the Raptor, I expect c* to be between 1879-2015 m/s. However the Raptor is likely to have more efficient combustion than the BE-4 because both propellants are expected to enter the combustion chamber as gases.  Available data published in textbooks puts the c* of LOX/CH4 at 1838-1857 m/s.  This puts the expected lower end of the BE-4 Isp at 308 sec @ SL and 344 sec @ vac.

What text books are you using to help guide your analysis?

Mostly Modern Engineering for Design of Liquid-Propellant Rocket Engines, by Huzel and Huang.

[Davidthefat]

Predicted BE-4 Sea Level Engine Performance

Property	Metric	Imperial	Uncertainty
Chamber Pressure	134 bar	1950 psi
Thrust at sea level	2,447 kN	550,000 lb
Thrust in vacuum	2,713 kN	609,924 lb	+/-0.8%
Specific Impusle at sea level	320 sec	320 sec	+/-5 sec	316+/-9 sec
Specific Impusle in vacuum	355 sec	355 sec	+/-3 sec	351+/-7 sec

I am adjusting my specific impulse prediction because the prediction was based on analyzing the SpaceX Raptor performance, specifically the characteristic exhaust velocity (c*). Based on the published design performance of the Raptor, I expect c* to be between 1879-2015 m/s. However the Raptor is likely to have more efficient combustion than the BE-4 because both propellants are expected to enter the combustion chamber as gases.  Available data published in textbooks puts the c* of LOX/CH4 at 1838-1857 m/s.  This puts the expected lower end of the BE-4 Isp at 308 sec @ SL and 344 sec @ vac.

What text books are you using to help guide your analysis?

Mostly Modern Engineering for Design of Liquid-Propellant Rocket Engines, by Huzel and Huang.

Liquid Rocket Thrust Chambers: Aspects of Modeling, Analysis, and Design is a good text I recommend.

[MikeM8891]

Predicted BE-4 Sea Level Engine Performance

Property	Metric	Imperial	Uncertainty
Chamber Pressure	134 bar	1950 psi
Thrust at sea level	2,447 kN	550,000 lb
Thrust in vacuum	2,713 kN	609,924 lb	+/-0.8%
Specific Impusle at sea level	320 sec	320 sec	+/-5 sec	316+/-9 sec
Specific Impusle in vacuum	355 sec	355 sec	+/-3 sec	351+/-7 sec

I am adjusting my specific impulse prediction because the prediction was based on analyzing the SpaceX Raptor performance, specifically the characteristic exhaust velocity (c*). Based on the published design performance of the Raptor, I expect c* to be between 1879-2015 m/s. However the Raptor is likely to have more efficient combustion than the BE-4 because both propellants are expected to enter the combustion chamber as gases.  Available data published in textbooks puts the c* of LOX/CH4 at 1838-1857 m/s.  This puts the expected lower end of the BE-4 Isp at 308 sec @ SL and 344 sec @ vac.

I realized I needed better c* data to predict the BE-4 Isp. I am going to trash the data based on Raptor because Raptor will be a gas-gas engine and the BE-4 definitely will not.  I am surprised by how efficient SpaceX expects the Raptor to be (c* = ~1950 m/s for Raptor vs ~1850 m/s textbook value) however this is inline with the expected efficiency increase between gas-gas and liq-liq hydrolox (c* = 2550 m/s vs 2416 m/s). Since the rocket engine power cycle has a great influence on the c*, I think the most accurate way to estimate the BE-4 c* may be to calculate the c* of oxygen-rich staged combustion kerosene rocket engines and adding 3.2% expected performance increase for using methane. I get 3.2% from comparing the textbook c* values of RP-1 and methane for SL engines.  As you can see from the below data this results in an average c* identical to the textbook value.  This data also revealed a trend of decreasing c* with increasing coefficient of thrust (Cf), see the attached graph. Using this trend and adding 3.2% performance increase for using methane, the Isp is 312+/-1 and 346+/-3 sec for SL an vac, respectively. The original post has been updated accordingly.

Textbook LOX/CH4 c* (also available on Wikipedia: Liquid rocket propellant)
1857 m/s for a SL optimized engine
1838 m/s for a vacuum optimized engine

Oxygen-rich stage combustion rocket performance

Rocket Engine	Cf	c* (m/s)	c* +3.2% (m/s)
YF-100	1.89	1743	1799
RD-170	1.86	1775	1832
RD-180	1.81	1825	1883
RD-190	1.79	1852	1912
Average	-	1799	1857

[ZachF]

Cool exercise. What mixture ratio are you assuming for this?