Generally, DELTA V = LN(MASS RATIO)* ISP*G That means that the Specific Impulse (ISP), or how much thrust you get from each pound of fuel is very important, and the Mass Ratio, or what percentage of your vehicle is propellant is less important. For each stage you can set an ISP to determine how much propellant you will use for the thrust you need. Then set a mass ratio to determine how much metal you wish to wrap around the propellant. The rule of Thumb is that higher stages get the better ISPs and Mass Ratios because they are smaller and they include the cost of the boosters. Boosters are the work horses, low ISP because of atmospheric back pressure, and heavy, but you can buy them by the pound cheap. Also, the ISP is set mostly by the propellant choice, the Mass Ratio on the other hand is determined by how much money you wish to spend on light weight materials. The lightest know material for construction is Unobtainium.
The booster (S0) terms consist of:
Weight, for the engines and the tanks. The weights are stated separately because engine weight for a booster is a major term. If you wish, you can zero out the engine weight and lump the weight under the tank term.
Propellant, remember to include enough to not run out.
Flow rate, the assumption here is that the engine uses fuel at a constant rate.
Thrust, this is the sea level thrust of the booster engines or main stage engines.
Expansion ratio thrust increase, this is the added thrust you expect to get due to the size of the nozzle and the reduction in atmospheric pressure with altitude. The program automatically adds the corrected thrust to the engine as the vehicle ascends. Ten percent is typical.
Drag area, this is the square footage of the forward aspect of the boosters. A 0.5 cd nose cone is assumed.
Stop seconds, the booster if used is assumed to start at launch, you must however tell the program when to shut down and jettison the boosters. The thrust, weight, and drag, are all adjusted at staging.
The main stage (S1) has the same terms, but adds a delayed start if you want to ignite the engine at altitude. It's not really a good idea, but some vehicles do it so I included the option here.
The second and third stages (S2, S3) do not allow separate engine weights. The weight of the engine for an upper stage is a smaller percentage of the weight. The start and stop times can delayed to allow the vehicle to drift between stages, but the times are required and must be defined even if the stage is not used.
The payload faring weight is included as a separate item because the program jettisons the faring at 200,000 ft.
Payload stack drag area is the square footage of the front aspect of the main stack.
Guidance, this is one of the areas that needs work. Several formulas are presented in the remarks in the program, but I'm still working on another. The problem is that there are lots of tricks that you can play with the guidance program. More updates later.
The Loft Factor is one of those tricks. It puts a kink in the flight path to use the booster to kick the upper stages high so that they can work to gain orbital velocity. It's something to play with.
Processor Delay, If you want to slow it down put in a bigger number.
And now an example. Booster mass ratio of 0.8, ISP 230, 100 Sec burn. 460,000# thrust, expansion ratio thrust gain 46000#. 1. propellant flow = 460,000/230 = 2000#/sec 2. 2000#/sec * 100 sec = 200000# total propellant 3. weight = (200000#/0.8)*(1 - 0.8)=50000# 4. the drag area depends on the density of the propellant and the finness ratio of the vehicle. You can figure it out or just make a good guess. My guess 100 sqft Main stage mass ratio of 0.8, ISP 230, 150 Sec burn, 115,000# thrust, expansion ratio thrust gain 23000#, pad ignition. Pretty much the same calculation. Second stage mass ratio of 0.9, ISP 310, 300 sec burn, 24000# thrust. ect. No third stage. Payload 200# to start. Faring 100# Payload drag 12 sqft. Loft factor 100The program will stop to allow you to change any of the variables that you might have messed up, type cont when ready. The data display appears with the rocket weight, and the attitude display in the upper right corner. When you type Y, the launch begins. Data will appear, and a velocity vector display will appear to the right. When the process has reached a conclusion, crash, out of propellants, or reaches orbit, the program stops to allow you to change variables and start over again.
BASIC FOR , WELL
Sorry, I started out with basic, well actually I started out with machine language on a Data General Nova. You will have to find a DOS file called gwbasic.exe, put it under an Icon in program manager. You can also use Qbasic.exe, but, the .bas file must be saved as an ASCII file, and Qbasic won't stop and wait when you get to a stop point in the program. You can also run the programs from the c:> prompt. When you start basic, type in "LOAD ROCKET48.BAS" if the file is in the same directory it should load "OK". then type "RUN". You can also use the function keys to operate basic, F1 = list, F2 = run, F3 = load, etc., they are usually labeled on the bottom of the screen. If you type in LLIST, basic will print out a copy of the program. To exit the program hit CTRL BREAK, then type SYSTEM to exit basic. You can run basic in a window under Windows, but it's very slow, while in basic hit ALT ENTER.
When this program was first written I ran it on a TRS Color Computer. Processor speed was 300k, and it took 15 minutes to complete a run with one second integration. The program has grown somwhat since then, and uses 0.1 second integration, it now takes a 486 the same 15 minutes to run the program.
Some notes about spacecraft reentry.
Weight of course is in pounds.
Square foot area is the blunt end for capsules, and the bottom for glide return. I added 10% for frontal drag on the glide return, and you can add drag devices also. The Space Shuttle uses "S" turns to lower itself into the atmosphere thereby increasing it's drag.
The CD is the shape factor of the capsule. 0.5 for slender, 0.8 for blunt.
The glide return section varies the angle of incidence to try to maintain a zero sink rate. This of course is only applicable for high altitudes. The numbers will not make sense below about 100,000 ft because the program does not use aerodynamic lift/drag parameters. Maybe the next version will roll it to a stop.
The heat/sqft indicator has no units, I got the formula from an Air Force Officers training manual (see the reading list) which did not go into great detail, probably best for officers.
For some historical input;
Mercury - 2460#, 30.17 sqft, CD 0.8, Drouge 31? @ 21000ft, Main 3115 @ 9800ft.
Gemini - 5952#, 46.54 sqft, CD 0.8, Drouge 54 @ 50000ft, Main 5565 @ 9800ft.
Apollo - 11700#, 128.6 sqft, CD 0.8, Drouge 427 @ 22966ft, Main 15147@ 9843ft.
Shuttle - 160000#, 3902 sqft, add some drag to get the sink rate right.
The program is set up to do a reentry from Earth orbit, of course if you really want to have fun, change the HV and VV at the CHANGE VARIABLES stop, remember that the program subtracts 500 ft/sec on startup so add 500 to your HV. VV=0 and HV=501 is great fun.
Mark Goll 19785 Marbach Lane San Antonio, Texas 78266 markgoll@wt.net http://web.wt.net/~markgoll