I've modified the atmospheric model to use the standard model upto 72 km, after that it's a vaccuum (the model 'ran out', but the atmosphere was down to <0.0001 kg/m^3 anyway up there.)
Disclaimers: optimising does not make it optimal, my program is very buggy, the rocket is very probably not physically realistic; rockets can go down as well as up ;-)
Simulation:
-----------
Vehicle is a 2 stage vehicle with 'challenging' dry mass and engines, it has approximately aspect ratio 6:1, or atleast the tank does, the nozzles are magically self altitude compensating, dunno how that works ;-), but they lose ISP at low alt. [I was planning to add multiple nozzles, but then I tried to work out how big they are, and I'm not sure I have room for even one] ;-(
There is that fun kink at the end of this run- the burn ends at about 113 degrees to the vertical, it's partly an artifact of how I plan the launch, partly it's the program circularising the orbit, and probably half a dozen other effects I'm not aware of, cos I'm only human, and my program isn't, oh yeah and my optimiser uses some randomness, that's probably why it takes off at -1.7 degrees.
Everthing is in SI.
Total Mass: 11854.750954402267
Fuel mass: 11426.149707063048
Payload mass: 50.0
Max Burn Size (N): 235954.63220708052
Height: 7.482853590914463
Diameter: 1.2471430046682705
Stage Ratio: 12.974752182091338
Engine Ratio: 13.200992811023474
tankmass: 114.26149707063048 engineMass: 199.03445367755353 miscMass: 57.13074853531524 deOrb: 7.853695637085353 subOrb: 0.035503538707456546
fuelMass/fuelDensity: 9.14091976565044
(oh yeah deOrb and subOrb are supposedly masses, they look too low, bug?)
Launch plan
------------
Distance From Launch: -1.0 angle: -1.8217332039022913 speed: 78.48861475449252
Distance From Launch: 64000.0 angle: -0.3007627229234393 speed: 114.56038935366333
Distance From Launch: 120000.0 angle: 1.8034679775004254 speed: 260.7716268355657
Distance From Launch: 240000.0 angle: 30.903354041462144 speed: 1014.2593645951055
Distance From Launch: 400000.0 angle: 99.25678307863579 speed: 4531.554268702643
Distance From Launch: 560000.0 angle: 93.56997461647913 speed: 13798.013967448807
Distance From Launch: 720000.0 angle: 99.32922546962305 speed: 15979.910785836995
Distance From Launch: 960000.0 angle: 139.6977166082601 speed: 0.0
Distance From Launch: 5.0E20 angle: 23.845994168111194 speed: 0.0
Simulation
-----------
(Key: t = time, a=altitude, as=air speed, mh=mach (below 71km), f=fuel mass, acc=acceleration (including gravity), mass=total mass, br=fuel burn rate(kg/s), dr=drag (g-force), vs=vertical speed, hs=horizontal speed, ang=angle to vertical, ts=target airspeed, th=throttle).
t:10.0 a:394.5 as:73.8 mh:0.2 f:10,742.2 acc:0.5 mass:11,174.2 br:67.8 dr:0.1 vs:74.0 hs:439.4 ang:-1.7 ts: 81.0 th: 1.0
t:20.0 a:1,200.2 as:81.4 mh:0.2 f:10,199.2 acc:0.0 mass:10,630.4 br:52.1 dr:0.1 vs:81.2 hs:438.2 ang:-1.6 ts: 83.5 th: 0.8
t:30.0 a:2,030.2 as:83.7 mh:0.3 f:9,688.2 acc:0.1 mass:10,119.4 br:53.9 dr:0.1 vs:83.4 hs:437.9 ang:-1.5 ts: 86.0 th: 0.8
t:40.0 a:2,883.4 as:85.2 mh:0.3 f:9,195.1 acc:0.1 mass:9,625.9 br:44.8 dr:0.1 vs:85.3 hs:438.1 ang:-1.4 ts: 88.5 th: 0.7
t:50.0 a:3,756.3 as:92.0 mh:0.3 f:8,705.7 acc:0.1 mass:9,136.9 br:52.4 dr:0.1 vs:92.0 hs:438.3 ang:-1.3 ts: 91.0 th: 0.7
t:60.0 a:4,652.3 as:91.8 mh:0.3 f:8,256.4 acc:0.7 mass:8,686.3 br:26.3 dr:0.1 vs:91.8 hs:438.8 ang:-1.2 ts: 93.6 th: 0.4
t:70.0 a:5,569.3 as:95.0 mh:0.3 f:7,815.4 acc:0.7 mass:8,245.3 br:25.8 dr:0.1 vs:95.0 hs:439.2 ang:-1.1 ts: 96.1 th: 0.4
t:80.0 a:6,509.7 as:99.6 mh:0.3 f:7,389.3 acc:0.6 mass:7,819.3 br:28.8 dr:0.1 vs:99.6 hs:439.6 ang:-1.0 ts: 98.6 th: 0.4
t:90.0 a:7,466.7 as:95.0 mh:0.3 f:7,006.2 acc:0.7 mass:7,437.4 br:53.6 dr:0.1 vs:95.0 hs:440.2 ang:-0.9 ts: 101.1 th: 0.8
t:100.0 a:8,457.2 as:95.4 mh:0.3 f:6,626.7 acc:0.2 mass:7,056.8 br:31.4 dr:0.1 vs:95.4 hs:440.7 ang:-0.8 ts: 103.7 th: 0.5
t:110.0 a:9,452.1 as:100.9 mh:0.3 f:6,260.3 acc:1.0 mass:6,691.6 br:55.2 dr:0.1 vs:101.0 hs:441.0 ang:-0.7 ts: 106.2 th: 0.8
t:120.0 a:10,482.5 as:108.8 mh:0.4 f:5,906.7 acc:0.9 mass:6,336.1 br:16.2 dr:0.1 vs:108.9 hs:441.4 ang:-0.5 ts: 108.8 th: 0.2
t:130.0 a:11,537.3 as:104.0 mh:0.4 f:5,596.4 acc:0.6 mass:6,025.9 br:19.0 dr:0.1 vs:104.1 hs:442.0 ang:-0.4 ts: 111.4 th: 0.3
t:140.0 a:12,606.6 as:103.3 mh:0.3 f:5,301.4 acc:0.2 mass:5,731.1 br:24.3 dr:0.0 vs:103.4 hs:442.4 ang:-0.3 ts: 113.9 th: 0.4
Plan changes at: 64012.96601353881 2
t:150.0 a:13,721.5 as:109.9 mh:0.4 f:5,007.2 acc:0.1 mass:5,437.2 br:28.0 dr:0.0 vs:110.1 hs:442.9 ang:-0.2 ts: 123.5 th: 0.4
t:160.0 a:14,942.6 as:121.8 mh:0.4 f:4,704.6 acc:0.0 mass:5,134.5 br:26.1 dr:0.1 vs:122.0 hs:443.5 ang:-0.0 ts: 135.4 th: 0.4
t:170.0 a:16,284.4 as:134.6 mh:0.5 f:4,401.2 acc:0.4 mass:4,831.5 br:33.4 dr:0.1 vs:134.7 hs:444.4 ang:0.2 ts: 147.5 th: 0.5
t:180.0 a:17,761.0 as:162.2 mh:0.5 f:4,078.8 acc:0.6 mass:4,509.3 br:38.5 dr:0.1 vs:162.4 hs:445.5 ang:0.3 ts: 159.7 th: 0.5
t:190.0 a:19,367.7 as:161.6 mh:0.5 f:3,808.0 acc:0.5 mass:4,237.5 br:19.1 dr:0.1 vs:161.7 hs:446.5 ang:0.5 ts: 172.0 th: 0.3
t:200.0 a:21,076.9 as:172.5 mh:0.6 f:3,539.0 acc:0.5 mass:3,969.0 br:30.2 dr:0.1 vs:172.5 hs:447.6 ang:0.7 ts: 184.4 th: 0.5
t:210.0 a:22,911.7 as:192.5 mh:0.6 f:3,276.4 acc:1.7 mass:3,707.1 br:42.9 dr:0.1 vs:192.6 hs:449.0 ang:0.9 ts: 196.9 th: 0.6
t:220.0 a:24,862.7 as:203.7 mh:0.7 f:3,047.3 acc:1.7 mass:3,477.9 br:40.0 dr:0.0 vs:203.8 hs:450.4 ang:1.1 ts: 209.5 th: 0.6
t:230.0 a:26,934.6 as:209.3 mh:0.7 f:2,845.6 acc:1.2 mass:3,275.6 br:30.2 dr:0.0 vs:209.3 hs:451.9 ang:1.2 ts: 222.3 th: 0.5
t:240.0 a:29,136.3 as:217.4 mh:0.7 f:2,660.7 acc:0.1 mass:3,090.1 br:16.7 dr:0.0 vs:217.3 hs:453.6 ang:1.4 ts: 235.2 th: 0.3
t:250.0 a:31,477.2 as:239.2 mh:0.8 f:2,480.0 acc:0.9 mass:2,908.9 br:6.8 dr:0.0 vs:239.1 hs:455.9 ang:1.6 ts: 248.4 th: 0.1
Plan changes at: 120022.36386170973 3
t:260.0 a:33,903.2 as:256.9 mh:0.8 f:2,322.1 acc:1.9 mass:2,752.2 br:30.9 dr:0.0 vs:256.8 hs:458.3 ang:1.9 ts: 262.8 th: 0.5
t:270.0 a:36,605.5 as:284.0 mh:0.9 f:2,157.8 acc:1.5 mass:2,587.6 br:26.0 dr:0.0 vs:283.6 hs:462.6 ang:3.1 ts: 295.4 th: 0.4
t:280.0 a:39,623.5 as:309.4 mh:1.0 f:1,994.9 acc:0.6 mass:2,424.4 br:17.7 dr:0.0 vs:308.6 hs:469.7 ang:4.4 ts: 329.1 th: 0.3
t:290.0 a:42,978.8 as:346.1 mh:1.1 f:1,829.7 acc:0.6 mass:2,258.7 br:8.8 dr:0.0 vs:344.6 hs:480.7 ang:5.8 ts: 364.1 th: 0.1
t:300.0 a:46,644.5 as:405.8 mh:1.2 f:1,663.3 acc:0.4 mass:2,092.4 br:10.1 dr:0.0 vs:402.7 hs:497.7 ang:7.2 ts: 400.6 th: 0.1
t:310.0 a:50,657.1 as:407.3 mh:1.2 f:1,551.3 acc:0.3 mass:1,980.5 br:11.6 dr:0.0 vs:402.6 hs:510.3 ang:8.7 ts: 438.9 th: 0.2
t:320.0 a:55,130.2 as:455.8 mh:1.4 f:1,425.2 acc:0.7 mass:1,854.4 br:12.5 dr:0.0 vs:448.1 hs:532.0 ang:10.3 ts: 479.7 th: 0.2
t:330.0 a:60,016.5 as:510.0 mh:1.6 f:1,313.2 acc:1.6 mass:1,742.6 br:16.2 dr:0.0 vs:498.0 hs:558.7 ang:11.9 ts: 523.1 th: 0.2
t:340.0 a:65,465.2 as:589.0 mh:1.9 f:1,203.2 acc:0.8 mass:1,631.9 br:2.0 dr:0.0 vs:570.6 hs:595.2 ang:13.7 ts: 569.9 th: 0.0
t:350.0 a:71,347.2 as:635.0 mh:100.0 f:1,123.2 acc:0.8 mass:1,551.9 br:0.9 dr:0.0 vs:609.1 hs:629.3 ang:15.7 ts: 619.9 th: 0.0
t:360.0 a:77,663.9 as:695.2 mh:100.0 f:1,049.3 acc:0.6 mass:1,478.0 br:1.8 dr:0.0 vs:658.9 hs:671.8 ang:17.7 ts: 673.6 th: 0.0
t:370.0 a:84,453.1 as:755.7 mh:100.0 f:979.2 acc:0.4 mass:1,407.9 br:2.9 dr:0.0 vs:706.2 hs:719.6 ang:20.0 ts: 731.6 th: 0.0
t:380.0 a:91,659.2 as:818.2 mh:100.0 f:912.4 acc:0.4 mass:1,341.1 br:3.5 dr:0.0 vs:752.1 hs:773.1 ang:22.4 ts: 793.6 th: 0.0
Stage separation at: 95841.98044062499
t:390.0 a:99,207.5 as:819.4 mh:100.0 f:876.4 acc:0.7 mass:961.5 br:0.8 dr:0.0 vs:738.4 hs:806.6 ang:24.9 ts: 859.8 th: 0.2
t:400.0 a:106,569.6 as:863.0 mh:100.0 f:837.3 acc:1.0 mass:922.7 br:5.1 dr:0.0 vs:759.2 hs:862.4 ang:27.6 ts: 927.5 th: 1.0
t:410.0 a:114,464.7 as:958.5 mh:100.0 f:786.0 acc:1.1 mass:871.4 br:5.1 dr:0.0 vs:821.3 hs:946.7 ang:30.4 ts: 1,001.2 th: 1.0
Plan changes at: 240044.75781796928 4
t:420.0 a:123,001.9 as:1,067.2 mh:100.0 f:734.7 acc:1.3 mass:820.1 br:5.1 dr:0.0 vs:887.0 hs:1,046.4 ang:35.5 ts: 1,251.6 th: 1.0
t:430.0 a:132,195.6 as:1,190.6 mh:100.0 f:683.4 acc:1.5 mass:768.7 br:5.1 dr:0.0 vs:952.1 hs:1,168.7 ang:41.6 ts: 1,563.5 th: 1.0
t:440.0 a:142,022.5 as:1,330.6 mh:100.0 f:632.1 acc:1.8 mass:717.4 br:5.1 dr:0.0 vs:1,013.1 hs:1,317.0 ang:48.3 ts: 1,908.4 th: 1.0
t:450.0 a:152,419.3 as:1,488.6 mh:100.0 f:580.8 acc:2.1 mass:666.1 br:5.1 dr:0.0 vs:1,065.2 hs:1,495.1 ang:55.7 ts: 2,290.7 th: 1.0
t:460.0 a:163,267.6 as:1,666.7 mh:100.0 f:529.5 acc:2.4 mass:614.8 br:5.1 dr:0.0 vs:1,102.1 hs:1,706.2 ang:63.9 ts: 2,714.6 th: 1.0
t:470.0 a:174,372.9 as:1,866.4 mh:100.0 f:478.2 acc:2.8 mass:563.5 br:5.1 dr:0.0 vs:1,115.0 hs:1,953.5 ang:73.1 ts: 3,184.1 th: 1.0
t:480.0 a:185,439.8 as:2,089.4 mh:100.0 f:426.9 acc:3.2 mass:512.2 br:5.1 dr:0.0 vs:1,092.2 hs:2,238.7 ang:83.1 ts: 3,702.6 th: 1.0
t:490.0 a:196,090.9 as:2,338.4 mh:100.0 f:375.3 acc:3.7 mass:460.7 br:5.1 dr:0.0 vs:1,018.6 hs:2,563.1 ang:94.3 ts: 4,275.5 th: 1.0
Plan changes at: 400001.24220195535 5
t:500.0 a:205,647.4 as:2,618.0 mh:100.0 f:324.0 acc:4.2 mass:409.4 br:5.1 dr:0.0 vs:888.0 hs:2,921.7 ang:98.7 ts: 5,497.7 th: 1.0
t:510.0 a:213,841.2 as:2,966.2 mh:100.0 f:272.7 acc:4.7 mass:358.1 br:5.1 dr:0.0 vs:752.0 hs:3,328.8 ang:97.6 ts: 7,292.4 th: 1.0
t:520.0 a:220,698.8 as:3,398.2 mh:100.0 f:221.4 acc:5.5 mass:306.8 br:5.1 dr:0.0 vs:621.1 hs:3,801.0 ang:96.3 ts: 9,277.8 th: 1.0
t:530.0 a:226,283.0 as:3,933.3 mh:100.0 f:170.1 acc:6.5 mass:255.5 br:5.1 dr:0.0 vs:497.9 hs:4,362.1 ang:95.0 ts: 11,503.3 th: 1.0
Plan changes at: 560220.5761184713 6
t:540.0 a:230,696.4 as:4,585.1 mh:100.0 f:120.4 acc:7.1 mass:205.7 br:4.6 dr:0.0 vs:388.8 hs:5,029.2 ang:93.7 ts: 13,853.8 th: 0.9
t:550.0 a:234,092.4 as:5,259.6 mh:100.0 f:79.5 acc:7.1 mass:164.7 br:3.6 dr:0.0 vs:289.5 hs:5,712.5 ang:95.5 ts: 14,533.5 th: 0.7
t:560.0 a:236,452.3 as:5,933.4 mh:100.0 f:46.8 acc:7.1 mass:132.1 br:2.9 dr:0.0 vs:181.1 hs:6,391.7 ang:97.5 ts: 15,299.1 th: 0.6
Plan changes at: 720144.9308962834 7
t:570.0 a:237,690.6 as:6,605.9 mh:100.0 f:20.8 acc:7.1 mass:106.0 br:2.3 dr:0.0 vs:65.8 hs:7,066.7 ang:101.4 ts: 15,141.6 th: 0.5
t:580.0 a:237,809.2 as:7,250.1 mh:100.0 f:0.8 acc:3.2 mass:85.9 br:0.8 dr:0.0 vs:-35.3 hs:7,711.0 ang:113.0 ts: 10,549.4 th: 1.0
t:600.0 a:237,026.8 as:7,280.0 mh:100.0 f:0.0 acc:0.9 mass:85.1 br:0.0 dr:0.0 vs:-39.1 hs:7,740.4 ang:137.5 ts: 857.8 th: 0.0
Plan changes at: 960046.8569934707 8
t:900.0 a:226,467.3 as:7,292.8 mh:100.0 f:0.0 acc:0.9 mass:85.1 br:0.0 dr:0.0 vs:-30.5 hs:7,753.0 ang:139.7 ts: 0.0 th: 0.0
t:1,200.0 a:219,108.0 as:7,302.7 mh:100.0 f:0.0 acc:0.9 mass:85.1 br:0.0 dr:0.0 vs:-18.0 hs:7,761.8 ang:139.7 ts: 0.0 th: 0.0
t:1,500.0 a:215,891.4 as:7,306.4 mh:100.0 f:0.0 acc:0.9 mass:85.1 br:0.0 dr:0.0 vs:-3.2 hs:7,765.7 ang:139.7 ts: 0.0 th: 0.0
t:1,562.0 a:215,792.8 as:7,309.0 mh:100.0 f:0.0 acc:0.9 mass:85.1 br:0.0 dr:0.0 vs:0.0 hs:7,765.8 ang:139.7 ts: 0.0 th: 0.0
Randall Clague wrote:
Ah, remember now. What he said.On Wed, 08 Jan 2003 17:09:40 -0800, "Tony Fredericks" <[EMAIL PROTECTED]> wrote:Actually, the best practice would be to have your vertical velocity fall to 0 as your horizontal velocity reaches orbital velocity for the selected altitude. Instant circularized orbit.When you do the trajectory sims, you find that the gravity turn trajectory that does this spends too much time in the atmosphere. A gravity turn that gets you out of the atmosphere at reasonable cost will, if it is not modified, put you in an orbit with an apogee several hundred km above the surface. And if you only just have enough energy to make orbit, then an orbit with apogee several hundred km above the surface has a perigee several hundred km below the surface.
And the planet. :-)This of course is hard on the vehicle.
But RLV = heat shields = aerobrakingI believe it was Andrew Case who called this maneuver "lithobraking." :-)
-R-- "You haven't been lost until you've been lost at Mach 3." -- Paul Crickmore _______________________________________________ ERPS-list mailing list [EMAIL PROTECTED] http://lists.erps.org/mailman/listinfo/erps-list
