Lecture 2: Presentation Materials February 8, 2010Posted by drspaceshow in Uncategorized.
Space Show Classroom Lesson 2: The Rocket Equation. Tuesday, February 9, 2010.
I. Presentation Material From Guest Panelist: Paul Breed of Unreasonable Rockets (http://unreasonablerocket.blogspot.com/).
Getting to Space is relatively easy, getting to orbit is hard.
The difference between Virgin and XCOR, etc… and Shuttle/SpaceX, etc…
Orbit means falling toward the earth, but going so fast you continually miss.
To get to orbit you to must go very very fast, the energy in orbit is 25x the energy on 100km suborbital hop.
You can almost think of it like the game tetherball, (http://en.wikipedia.org/wiki/File:Tetherball_flickr.jpg) A suborbital hop just pushes the ball straight out from the pole, it then falls back to the poll. If you really hit the ball it goes around the pole.
The absolute minimal possible orbital velocity is 7500 m/sec. (17000 mph)
This means your rocket must impart 7500 m/sec of horizontal velocity.
Any real world vehicle with drag will have higher requirements.
A very very large rocket could get close to 7500 m/sec but a very small rocket could easily require 10000 m/sec DV to counter the air drag.(1)
To go that fast a rocket needs to be mostly fuel.
It will also stage as this lets it drop the empty tank stage and big motors.
The Sci fi rockets like the Star Wars fighters, Star Trek shuttle, comic book rockets etc.. are not possible with chemical propulsion. We will never ever have a chemical powered orbital rocket that looks like a commercial air plane.
All orbital chemical rockets will look like a flimsy flying gas tank.
The very best commercial plane carries 1/2 its weight in fuel.
An orbital SSTO rocket needs to be more than 95% fuel mass. The other % must include structure, motors, and payload.
And its even worse than it seems for every pound of fuel a jet burns it uses 10 lbs of “free” air. A Rocket needs to bring along its own “air/oxidizer” and that is the definition difference between rockets and jet.
A rocket is not like a car where it pushes on the immoveable road to make it go forward. A rocket is like sitting on a row boat in the middle of the lake and throwing baseballs out the back to make it go forward. Probably works better if Roger Clemons is throwing.
Works really well if the baseball was shot out of cannon….. (cannons are heavy so there is a point of no return.)
In a rocket the baseballs are gas molecules and they are thrown very fast. The speed the balls are thrown are usually called ISP. higher pressures more complex motors can throw faster, but just like a cannon. If they get too heavy there is a point of diminishing returns.
The actual equation : delta V = Ve * ln (Mi/Mf)
Delta V = The change in velocity.
Ve = The exhaust velocity of the propellant leaving the rocket.
Mi = The initial Mass of the vehicle. (The empty wt + payload + propellant)
Mf = the final Mass of the vehicle. (The empty wt+ payload + reserves)
ISP (in seconds) = Ve/acceleration due to gravity
The 180 second LLC vehicles had an achieved delta V of 9.8m/sec * 180 = 1764 m/sec
(Minimal orbital is 7500 m/sec) 4.5 times as much dv, and it is logarithmic relation ship at least 20 times harder.
Using same level of performance as Masten’s LLLC vehicle carrying a 55lb payload (Assume 55lbs payload GLOW of 855lbs and hover of 195 seconds)
would require 4 stages and stages with equal DV per stage 1st stage would weigh more than 3M pounds. So the performance of a real useful orbital rocket needs to be much higher than the LLC vehicles.
Its not really quite that bad as when you gain altitude and don’t have to throttle the ISP performance improves significantly. But for the same level of technology that answer is within an order of magnitude.
This is why SSTO is almost impossible.
|Performance/Vehicle Class||ISP||Dry Mass to reach orbit|
|Improved LLC class||250||3.9%|
*Both SSME and NERVA used Liquid Hydrogen, hard to get good mass ratio with LH2 as it has the density of an empty Styrofoam cup Hydrocarbon Fuels require a higher mass fraction, but are much denser actually making the mass fraction easier to achieve.
Chemical rockets will remain expensive until you can reuse them, and the rocket equation makes that very hard.
The only way to get both high thrust and high ISP is either some form of external power like the Laser Launch scheme, or some form of nuclear power, fission, fusion etc…
Some electric propulsion system have very high ISP’s but they have very low thrust to weight, i.e. 1/1000th or less. So they can not climb out of the gravity well to LEO.
Long term LEO access can be somewhat solved with very large engineering projects, like the space elevator, Loftsrom loop (http://en.wikipedia.org/wiki/Launch_loop) to get to low earth orbit and nuclear propulsion, preferably fusion for going from LEO onward.
In the short term one might see some benefit from rotavators or other tether schemes. Based on what I know, the space elevator has big material and stability issues. The loop has a physically larger footprint on the ground but requires no new materials.
If one could generate a machine with 50% energy efficiency getting a human to orbit would require less than $200 of energy at current electrical energy rates.
90Kg * 8000 m/sec^2 * 50% = 2880 MJoules = 800 Kilo watt hours
At 10c a kwa = $80.00
I really like the Orion concept, but humans have become very risk adverse, the open air atomic bombs would be unpopular. ;-(
(1) https://e-reports-ext.llnl.gov/pdf/321763.pdf How Small can a Launch Vehicle Be AIAA 2005-4506.
II. Presentation Material from Co-Host Dr. John Jurist:
The Rocket Equation: Delta-V = Ve * ln (Mi / Mf)
Delta-V = The change in velocity of the rocket in absence of gravitational and aerodynamic losses.
Ve = The exhaust velocity of the propellant leaving the rocket.
ln = Natural logarithm = loge
Mi = The initial mass of the vehicle. (empty wt + payload + propellant)
Mf = The final mass of the vehicle. (empty wt + payload + reserves)
Isp = Specific Impulse (in seconds) is Ve /acceleration due to gravity. In English units, it is the pounds of thrust generated by a specific propellant combination at a burn rate of one pound per second.
Some implications of the rocket equation are considered below:
One reason an orbital launcher will not look like a commercial airplane is wings and landing gear – used mostly for landing but very heavy to carry up to orbit. If the vehicle takes off from the ground, the landing gear must be sized for the takeoff weight. The Shuttle gear is sized for the landing weight because the STS launches vertically. Also, loads on an airplane are mostly transverse. If an aerospace plane launches horizontally, the loads will switch from transverse during takeoff and initial climb out to mostly longitudinal during the higher altitude and orbital insertion portions of the flight. The loading then switches back to mostly transverse for re-entry and landing. In contrast, vertical takeoff rockets have mostly longitudinal loads and can be built lighter. That improves the potential payload fraction.
Horizontal air launch potentially adds drag losses during the initial flight envelope and also the vehicle requires more robust structure relative to a conventional vertical takeoff rocket in order to tolerate the pitch up maneuver as it starts the atmospheric climb out.
Because air has oxygen, many people suggest a combined jet/rocket engine (or separate jet and rocket motors) to reduce the quantity of oxidizer to be carried on board an orbital launcher. One of several problems with this approach is that the thrust to mass ratio of a rocket motor is much greater than that of a jet engine. The mass penalty for an air breathing launch vehicle ends up very severe and in practice exceeds the advantage of using ambient oxygen.
Examination of the rocket equation shows that increasing exhaust velocity improves things. Liquid fluorine-liquid hydrogen has better exhaust velocity than liquid oxygen-liquid hydrogen, but is too toxic to be feasible. Liquid oxygen-liquid hydrogen is the best we have in terms of exhaust velocity, but hydrogen’s low density and insulation requirements are both issues.
In a two stage launcher, first stage performance isn’t quite as critical as is second stage performance. This drives the use of liquid hydrogen in second stages with hydrocarbon fuel in the first stage.
When considering the payload fraction of a launch vehicle, there are some scaling problems that come into play as vehicle size changes. For smaller vehicles, the surface to mass ratio is increased and aerodynamic losses become relatively more significant. The propellant fraction of the vehicle tends to be reduced because of tank volume/area considerations and relatively fixed masses associated with motors, pumps, plumbing, etc.
Over the years, aerospace engineers have developed numerous parametric relationships to estimate the inter-relationships of masses of different components as a function of overall size. These relationships not only relate structural mass to propellant mass, for example, but relate many of these parameters to development cost and to production cost. A good source for those who wish to dig into this pragmatic aspect of rocket engineering in more detail is a book by Dietrich Koelle: Handbook of Cost Engineering for Space Transportation Systems. It is published and sold by Microcosm.
The bottom line is that a developed launch vehicle is the result of countless technical tradeoffs and compromises. A few of the variables that are involved include:
- Delta-V budget between stages,
- Propellant combination, boil off rate for cryogenic propellants, etc.
- Launch trajectory (tradeoffs of gravity and aerodynamic losses versus burn time and vehicle acceleration),
- Propellant pumps versus pressure-fed propellants,
- Ablatively cooled versus regeneratively cooled motors,
- Composite versus metal tanks,
- Multiple small motors versus few larger motors,
- Structural issues related to steady state wind shears and gust loading, and
- Tolerance of payload for acceleration profile, vibration and noise environment.
All of these variables and more must be considered in light of the vehicle or program lifecycle (spreading development costs over the number of anticipated launches). In addition, risk analyses must be done that determine insurance costs for general liability and for potential payload losses.