Copyright 2016 Robert Clark
(patents pending)
Some calculations show a surprising increase in the amount of payload that can be carried by a single-stage-to-orbit rocket (SSTO) by using altitude compensation [1], such as the aerospike, even multiple times more than possible without it. Indeed, the calculations revealed that for an already high propellant fraction stage such as the Falcon 9, alt. comp. gives the SSTO a better cost per kilo ratio than the two stage rocket (!)
This was a surprising result since during much of the era of orbital rockets it was received wisdom that SSTO's were not technically feasible. Then, it gradually became accepted it could be done, but it was then felt it would not be worthwhile because of the small payload. Therefore it is quite remarkable that the exact opposite of this is true, the SSTO is more cost effective than the TSTO (two-stage-to-orbit) when using altitude compensation [1].
But the usefulness of altitude compensation is not just for SSTO's. The payload for a two-stage to orbit launcher can be increased 25% by using it [2]. And triple-cored rockets such as the Delta IV Heavy, and Falcon Heavy can have their payload doubled when using altitude compensation in concert with cross-feed fueling [2]. Moreover, by using alt. comp., simple pressure-fed stages that are within the technical means of most university engineering departments can be made to make suborbital [3] and orbital launchers [4].
However, an argument has been made that transforming already existing engines to altitude compensation such as the aerospike would be expensive since it would require changing the combustion chamber to a toroidal shape. Then I investigated other means of achieving altitude compensation other than the aerospike [5].
One of these methods was to use high temperature carbon nanotube "rubber" [6] as a nozzle extension. This could be attached to the nozzle of already existing engine nozzles and be variably extended as the rocket gained altitude.
But could we use metals for this purpose? The metal would have to be stretchable as is rubber to become twice as long or more as the nozzle is extended. Normally though metal can only be stretched by a fraction of its original length before fracturing and even then it takes quite a large amount of force to do the stretching.
There is a scenario though where metals can be stretched for a longer length and at a small amount of required force, that is at elevated temperatures. This is through forging. This takes place while the metal is still solid. The forging temperature [7] is where the metal is more malleable but below the melting temperature. It is commonly in the range of 60% of the melting temperature. Then the idea would be as the nozzle becomes heated as the engine is firing it would become more and more easily extended further out.
For how to extend, that is stretch, the nozzle, one possibility would be to use high pressure inert gas such as helium injected within the hollow walls of the nozzle to stretch it you as would for blowing up a a hollow balloon. Another would be actuators attached to the end to stretch it out.
For either method you would want the nozzle to maintain the usual bell nozzle shape. You could have the wall thickness vary along the nozzle's length so that as it is stretched out the required shape is maintained. You might also have ribs along the vertical length of the nozzle to help encourage the stretching to proceed in the desired direction.
Another consideration is that you don't want the nozzle to reach a degree of heating so that it reaches the melting point. An interesting fact about rocket nozzles and combustion chambers is that they actually operate at temperatures above the melting point of the metal composing them. The reason why they don't melt is that for a material to undergo the phase change from solid to liquid, not only does the temperature have to be at the melting point, but a sufficient quantity of heat dependent on the material has to be supplied to the material, the enthalpy of fusion [8].
Then rocket engines have cooling mechanisms applied to the chamber and nozzle walls to draw away the heat supplied by the combustion products so that this amount of heat is never applied to chamber and nozzle. One key method that is used for high performance engines is regenerative cooling. This is where the fuel is circulated through channels in the walls of the engine to draw away the heat.
Another factor to limit the temperature and heat applied to the nozzle is that this is envisioned as an attachment to a usual, static nozzle. However, as the engine exhaust is expanded out by a bell nozzle the temperature drops. So for the attachment at the bottom of the usual nozzle, the temperatures it would have to withstand would be reduced.
A diagram showing the stress-strain curve at elevated temperatures for titanium alloys is here [9]:
The strain at room temperature is commonly only a fraction of a percent, ca. 0.2%, or 0.002. But here at elevated temperatures in the range of 800C to 1,050C, we see the strain can reach .7, and likely above with continued pressure applied.
REFERENCES.
1.)Thursday, November 7, 2013
The Coming SSTO's: Falcon 9 v1.1 first stage as SSTO, Page 2.
2.)Monday, January 11, 2016
Altitude Compensation Improves Payload for All Launchers.
3.)Thursday, January 15, 2015
NASA Technology Transfer for suborbital and air-launched orbital launchers.
4.)Thursday, August 13, 2015
Orbital rockets are now easy.http://exoscientist.blogspot.com/2015/08/orbital-rockets-are-now-easy.html
5.)Saturday, October 25, 2014
Altitude compensation attachments for standard rocket engines, and applications.
http://exoscientist.blogspot.com/2014/10/altitude-compensation-attachments-for.html
6.)Carbon Nanotube Rubber Stays Rubbery in Extreme Temperatures.
Liming Dai
Angew. Chem. Int. Ed. 2011, 50, 4744 – 4746
http://case.edu/cse/eche/daigroup/Journal%20Articles/2011/Dai-2011-Carbon%20Nanotube%20Rubb.pdf
7.)Forging temperature.
https://en.wikipedia.org/wiki/Forging_temperature
8.)Enthalpy of Fusion.
https://en.wikipedia.org/wiki/Enthalpy_of_fusion
9.)MODELLING HIGH TEMPERATURE FLOW STRESS CURVES OF
TITANIUM ALLOYS
Z. Guo, N. Saunders, J.P. Schillé, A.P. Miodownik
Sente Software Ltd, Surrey Technology Centre, Guildford, GU2 7YG, U.K
http://www.sentesoftware.co.uk/media/2524/flow_stress_curve.pdf
