Copyright 2016 Robert Clark
It is unfortunate that SSTO's have been, incorrectly, deemed unviable. Since altitude compensation has only been thought of in terms of improving the payload of SSTO's, little research has gone into these methods, as SSTO's were not considered worthwhile.
However, in point of fact altitude compensation improves the payload even for multistage rockets. In the blog post "The Coming SSTO's: Falcon 9 v1.1 first stage as SSTO, Page 2", I showed using the payload estimator by Dr. John Schilling altitude compensation improved the payload of the two-stage Falcon 9 by 25%.
Interestingly, the increase for the case of a rocket with side boosters can be as high as 40%. This is the case for the Delta IV Heavy.
According to this page the payload to LEO of the Delta IV Heavy is 25,980 kg:
Delta IV Heavy – RS-68A Upgrade.
Using the specifications from this page and inputting the vacuum values for the thrust and Isp, since the Schilling calculator requires inputting the vacuum values as it takes into account the diminution at sea level, the calculator appears as:
And the results are:
| Launch Vehicle: | User-Defined Launch Vehicle |
|---|---|
| Launch Site: | Cape Canaveral / KSC |
| Destination Orbit: | 185 x 185 km, 28 deg |
| Estimated Payload: | 23979 kg |
| 95% Confidence Interval: | 19412 - 29682 kg |
"Payload" refers to complete payload system weight, including any necessary payload attachment fittings or multiple payload adapters
This is an estimate based on the best publicly-available engineering and performance data, and should not be used for detailed mission planning. Operational constraints may reduce performance or preclude this mission.
A rather close approximation to the actual payload.
Now we'll consider the result when altitude compensating nozzles are used. First, note that there are numerous low cost methods of accomplishing altitude compensation. For instance the RL-10 engine increases its vacuum Isp to ca. 464 s simply by attaching a nozzle extension. Other low cost methods are discussed in "Altitude compensation attachments for standard rocket engines, and applications."
Increasing the vacuum Isp to 464 s increases the thrust proportionally to (464/414)*3560 = 3,990 N. Then the inputs to the calculator now appear as:
This gives the result:
| Launch Vehicle: | User-Defined Launch Vehicle |
|---|---|
| Launch Site: | Cape Canaveral / KSC |
| Destination Orbit: | 185 x 185 km, 28 deg |
| Estimated Payload: | 33410 kg |
| 95% Confidence Interval: | 27137 - 41212 kg |
"Payload" refers to complete payload system weight, including any necessary payload attachment fittings or multiple payload adapters
This is an estimate based on the best publicly-available engineering and performance data, and should not be used for detailed mission planning. Operational constraints may reduce performance or preclude this mission.
About 40% higher than the case without altitude compensation. The reason why it should be expected the increase is higher than in the standard two-stage case is the center core stage in a triple-core launcher spends more of the time at high altitude where the vacuum Isp would obtain.
Altitude Compensation plus Cross-feed Fueling.
This effect should be even more pronounced with cross-feed fueling. Cross-feed means the center core stage would have its full propellant load after the side boosters are jettisoned so it spends even more time at vacuum conditions.
The Schilling calculator emulates cross-feed by inputting 2/3rds of the actual propellant load in the field for the side boosters, but increases the value input for the center core propellant to (1 +2/3) times the actual value (See discussion here for an explanation of how the calculator emulates cross-feed.)
The results are:
| Launch Vehicle: | User-Defined Launch Vehicle |
|---|---|
| Launch Site: | Cape Canaveral / KSC |
| Destination Orbit: | 185 x 185 km, 28 deg |
| Estimated Payload: | 48961 kg |
| 95% Confidence Interval: | 41112 - 58206 kg |
"Payload" refers to complete payload system weight, including any necessary payload attachment fittings or multiple payload adapters
This is an estimate based on the best publicly-available engineering and performance data, and should not be used for detailed mission planning. Operational constraints may reduce performance or preclude this mission.
This is double the initial payload capability without cross-feed and altitude compensation. Note also Cross-feed fueling is not an unknown technology having been used on jet aircraft such as the Concorde for decades and also on the Space Shuttle's OMS engines.
And For the Falcon Heavy?
This payload for the upgraded Delta IV Heavy would rival the announced 53 metric tons(mT) LEO payload of the Falcon Heavy with cross-feed fueling and exceed that of the FH without it. But the increase in thrust of the Merlin 1D and increase of propellant load should increase the LEO payload of the Falcon 9 and Falcon Heavy. If the payload to geostationary for the F9 is increased by 30% as announced by SpaceX, then we expect the payload to LEO for the F9 and Falcon Heavy also to be increased a similar amount.
Then the current upgraded Falcon Heavy with cross-feed may now be in the 70 mT range. And if altitude compensation also gives this triple-cored launcher a 40% increase in payload that would bring it to the 100 mT range. This is important because this is the range estimated to be required for a manned lunar lander mission by a single launcher, and would be one in a cost range of only $120 million.
Bob Clark
3 comments:
The SLS would be under major pressure if the Falcon Heavy can lift 100 mT for $120 million.
I would doubt these numbers.
The engines start off with expansion ratios of 21.5 while upper stage has expansion ratio of 250. Adding extensions would increase mass by a few tons per core.
Second point is that calculator does not accout for the fact that the rocket would still start with usual expansion ratio. What is the altitude where switch would be done? 10km? 20? By that time the rocket would burn about half of the fuel in the boosters. With that sea level isp...
Given that expansion ratio on D4H is 21.5 with nozzle diameter of 2.34m and that booster core diameter is 5.1m, maximum expansion ratio would be about 80. According to thrust coefficient curves I have that would put vacuum isp at 436s.
But at 10km, a 21.5 expansion ratio nozzle still has more thrust than ratio 80 nozzle.
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