*Copyright 2014 Robert Clark*

In the blog post "Altitude compensation attachments for standard rocket engines, and applications", I noted that the idea that altitude compensation was only useful for SSTO's prevented their implementation and therefore their usefulness for multi-stage rockets was not realized.

An example of this is Orbital Sciences Antares rocket. The failed flight of the Antares in October, 2014 put renewed emphasis on the choice of 1960's era Russian engines AJ-26/NK-33. It is understandable why they were used since on the key performance metric of Isp, at 330+ s they were significantly better than American engines, at ca. 300 s.

However, by using altitude compensation the Isp of the low performance American rocket engines can even exceed that of the Russian engines. Orbital Sciences has decided not to use anymore of the Russian-derived engines on the Antares, and therefore need a replacement engine. I suggest investigating altitude compensation attachments that can made to already existing American engines so would be relatively low cost to implement.

One possible engine that could be used would be the Rocketdyne RS-27A. It is used on the venerable Delta II rocket. Rocketdyne claims a 100% reliability record for the engine. You would need three of them though at ca. 200,000 lbs. thrust to make up for the two AJ-26/NK-33 engines at ca. 300,000 lb. thrust.

How high could we get with the Isp on the RS-27A using altitude compensation? At an area ratio of only 12 to 1, the RS-27A only gets a vacuum Isp of 302 s. To see how much better we can do with a larger nozzle, we might make a comparison to the Russian RD-58, which gets a vacuum Isp of 349 s by using a high area ratio of 189 to 1 with not a particularly high chamber pressure of 78 bar. A better comparison might be to the Russian RD-0124 with a vacuum Isp of 359 s, but at a high chamber pressure of 162 bar. Unfortunately the area ratio of this engine is not specified, but it is certain to be high since it is an upper stage engine.

Actually for

Support for the idea a high area ratio on a kerosene engine can get a vacuum Isp of ca. 360 s even with a low chamber pressure is provided by the Rocket Propulsion Analysis program. Using the free Lite version you can estimate some fairly accurate

Actually for

*vacuum*Isp, just having a high nozzle area ratio is more important than the chamber pressure, a high chamber pressure being needed to insure a high*sea level*Isp. As a point of comparison, the hydrogen fueled RL-10B2 has only a chamber pressure of 39 bar but by using a nozzle extension to bring the area ratio to 280 to 1, it gets the highest Isp of any chemical engine at 465.5 s.Support for the idea a high area ratio on a kerosene engine can get a vacuum Isp of ca. 360 s even with a low chamber pressure is provided by the Rocket Propulsion Analysis program. Using the free Lite version you can estimate some fairly accurate

*vacuum*Isp's for rocket engines, the sea level estimates though for the free version being not so accurate. Here are results using the specifications given on the Astronautix page on the RS-27A:
The "Optimum Expansion" Isp number I've found to be a relatively accurate estimate for the actual vacuum Isp of existing engines. By the way, the negative values for the "Sea level" Isp are coming from the fact there would be severe losses for a low chamber pressure engine using such a large expansion ratio nozzle.

Now compare this to the results if the chamber pressure were say 160 bar:

You see the large increase in chamber pressure only adds minimally to the vacuum Isp, though it would have a great effect on the sea level Isp.

So we'll take the vacuum Isp of the RS-27A with an adaptive nozzle attachment as 360 s. Now to calculate how much payload we can get on the Antares with these new engines I'll use the original's dry mass and propellant mass specifications here: Antares Launch Vehicle Information. The dry mass of the first stage is given as 18,700 kg and the gross mass as 260,700 kg.

The two AJ-26 engines weighed 1,200 kg each for a total of 2,400 kg. The RS-27A weighs 1,000 kg, So three will be 3,000 kg. So the dry mass raises to 19,300 kg and the gross mass to 261,300 kg. I am assuming the adaptive nozzles can be made lightweight so as not to significantly increase the engine weight. The three RS-27A's though will have a lower liftoff thrust than the two AJ-26's. To make up for that I'll use a higher efficiency upper stage such as the hydrogen-fueled Ariane 4 H10-3 rather than the solid Castor stage now used.

Now consider that we are assuming our adaptive nozzle will allow near optimal expansion from sea level to vacuum. Then note the RS-27A is a later edition of the RS-27 where the area ratio was increased from 8 to 1 to 12 to 1 to improve the vacuum Isp. But this reduces the sea level performance. The sea level Isp and thrust were reduced from 264 s and 93,357 kilogram-force (kgf) for the RS-27 to 255 s and 90,770 kgf for the RS-27A. But considering our adaptive nozzle I'll assume we are able to also get the 264 s Isp and 93,357 kgf thrust at sea level or perhaps do even better with a shorter nozzle equivalent at sea level.

At a 93,357 kgf liftoff thrust the total thrust at liftoff would be 280,071 kgf. The H10-3 stage has a gross mass of 13,100 kg. Then the total mass without payload will be 261,300 kg + 13,100 kg = 274,400 kg. This would result in a rather low thrust/weight ratio at liftoff which will reduce payload capacity through gravity drag.

A couple of ways to improve this liftoff T/W ratio. First note on the page on the Antares linked above the specifications include the thrust at 108% of the "rated thrust". This is rather common that an engine can actually operate at a few percentage points above its rated thrust. This is the case for example with the Space Shuttle Main engines. If the RS-27A with adaptive nozzles can operate at 108% of its rated thrust that would bring the sea level thrust to 302,476 kgf.

Another way to improve the liftoff T/W would be to reduce the propellant load by say 20,000 kg. As we'll see below the payload would still be rather high.

We'll use Dr. John Schilling's launch performance calculator to estimate the payload possible. Select the Wallops launch site in the calculator and input the "inclination, deg" as 38, to match the Wallops site latitude.

The calculator uses the vacuum values for the Isp and thrust inputs. This will be raised to 360 s for the Isp with our adaptive nozzles. But note also this increase in vacuum Isp also results in an increase in the vacuum thrust by a factor of the ratio of the Isp's, that is, by a factor of 360/302. Then the three RS-27A with adaptive nozzles will have vacuum thrust (360/302)*3*1054.20 kN = 3,700 kN.

Input also the specifications for the Ariane 4 H10-3 for the second stage in the calculator. The HM7-B engine used on that stage has a vacuum Isp of 447 s. Then the results are:

Launch Vehicle: | User-Defined Launch Vehicle |
---|---|

Launch Site: | Wallops Flight Facility |

Destination Orbit: | 185 x 185 km, 38 deg |

Estimated Payload: | 9458 kg |

95% Confidence Interval: | 7735 - 11589 kg |

The estimate of 9,458 kg is nearly twice the payload of the current Antares. Notably though this is using the high efficiency hydrogen-fueled upper stage.

To address the low liftoff T/W I mentioned one way was to reduce the propellant load by, say, 20,000 kg. Doing this results in a payload of:

Launch Vehicle: | User-Defined Launch Vehicle |
---|---|

Launch Site: | Wallops Flight Facility |

Destination Orbit: | 185 x 185 km, 38 deg |

Estimated Payload: | 8764 kg |

95% Confidence Interval: | 7166 - 10736 kg |

Still a pretty high result.

A consideration in regards to the accuracy of this estimate however is the effect of the altitude-compensating high vacuum Isp compared to the assumptions that go into the calculator. The Schilling calculator takes the vacuum Isp and thrust as inputs and automatically takes into account the reductions at sea level. However, since it assumes it is using a fixed nozzle it would assume the sea level Isp and thrust are much closer to the vacuum values than they would be in this scenario. On the other hand the altitude compensating nozzle would not have the losses of a fixed nozzle. Then more accurate payload calculators that take into account the variations of Isp and thrust with altitude would need to be used to get a more accurate estimate of the payload to orbit.

Bob Clark

## 1 comment:

Rocket motor nozzles work at all because of pressure drop chamber to ambient. Thrust in vacuum (stream momentum plus an exit plane pressure term) minus the back pressure term Pamb*Aexit IS the thrust at any altitude (including sea level ) AS LONG AS an overexpanded nozzle is not separated.

For an overexpanded nozzle, the backpressure term Pamb*Ae is larger than the exit-plane pressure term (Pe*Ae).

Up to a point, this backpressure correction term works. That point is where flow separates from the nozzle walls. There are empirical equations that roughly predict when separation occurs. Once flow separation occurs, there are no models that correctly compute thrust in that separated-flow nozzle.

You can size an expansion bell to operate overexpanded but unseparated at sea level, which for a given design puts perfect expansion up at some altitude. Above that altitude the exit plane pressure > ambient, and the net exit plane pressure term (Pe - Pamb)*Ae) term adds to (instead of subtracting from) vacuum thrust.

Overall delivered impulse-wise, you do better if you size first stage engine bells for perfect expansion (Pe = Pamb) at sea level, and get a positive addition from the net static pressure term (Pe - Pamb)*Ae all the way up.

Aerospike nozzles allow you to avoid overexpanded flow separation, because the plume flow cross section adjusts to "perfect expansion" by shrinking or swelling in size. The penalty is lower thrust efficiency, because there is less solid material in contact with the expanding plume.

GW

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