From v03.n1219 Fri Oct 3 12:24:41 1997 From: Anthony Jackson Date: Mon, 16 Jun 1997 11:53:25 -0700 (PDT) Subject: V2E: missile design Hm...the rules for missiles in Vehicles make no sense; here's an attempt at saner rules (consistent with other tech in Vehicles, and with normal drag, etc); comments welcome. Missiles: v0.1 Design Sequence: remove choosing spd; this is done later. No other changes. Performance: 1) Determine I (total impulse, in G-seconds). This is equal to: K*(2-log(10+P)), where P is the % of the missile weight which is payload, and K is a TL-based constant (equal to 2.3*Isp, for those who wish to invent their own rockets). Using Vehicles solid-fuel rockets, K is 70 at TL 3-4, 450 at TL 5, 550 at TL 6, 700 at TL 7, 820 at TL 8 (numbers adjusted to assume a 5-10% propellant casing weight instead of 15%; at 15% TL 7 solid fuel rocket propellant has an Isp of 336, which is a bit high) 2) For space missiles, choose G (acceleration, in gravities). E is equal to I/G. 'Range' (guided range) is equal to 5.5 * I * E. 3) For air-based missiles, choose Spd. Spd cannot exceed 8 * I, due to requirements for reaching full velocity. Spd is in yards/second. For an air/space missile, see below. 4) Compute D (drag, in Gs), which is equal to 1 + (spd/100)^2/weight^(1/3). If used in space, D will be the number of Gs of acceleration the missile will have. Alternately, a space missile used in atmosphere will have a speed equal to weight^(1/6)*sqrt(G-1)*100, which gives D=G. A guided atmospheric missile may have fins; reduce D by 1, but D cannot be lower than 1. Unguided missiles and air/space missile do not have fins. 5) Compute E (endurance), which is equal to (I-Spd/10)/D. 6) Compute 'half-damage' range, equal to E*Spd. This is the range at which the engine burns out, and is thus usually the maximum range for guided missiles. Accurate range may be much lower; compute Acc based on Spd. 7) Compute 'max' range, equal to 1/2D + Spd^2/(10*D). 8) All other stats are identical to Vehicles rules. Example 1: TL 7 air to air missile, 190 lb (comparable to a sidewinder). Payload: 21 lb warhead, ? lb IRH guidance (say, 8 lb). Payload 29 lb(15%) I = 700 * (2 - log(25)) = 420. Spd = 900 (mach 2.5). D = 81/5.75 = 14. E = (420-90)/14 = 24. Range 22,000 (12 miles). Example 2: TL 8 unguided 15mm APEX rocket, standard warhead (gyroc). Wt 0.135. Payload: jumbo 15mm APEX (0.54 lb, 40%). Explosive damage 1d+3. I = 820 * (2 - log(50)) = 246. Spd = 425 (KE damage 8d). D= 1+18/.51=36. E = (246 - 42)/36 = 5.7. 1/2D 2400, Max 2400+(425)^2/360=2900 Example 3: TL 8 air/space missile, 200 lb w/30 lb payload. I = 820 * (2 - log(25)) = 490. Space: G = 10. E = 49. Range = 130,000 Air: spd=2.42*3*100 = 725. E = (490-72)/10 = 42. Range = 30,000 (17 mi) Special rule: multi-stage rockets, late TL 6. Simple computation tells us that the maximum total impulse for a TL 7 rocket is 700 (at 0% payload), which is insufficient to reach orbit. The problem is, of course, that the weight of the rocket itself is considerable. A classic solution to this problem is multi-stage rockets. A multi-stage rocket is basically a light rocket which is a payload within a heavier rocket; it can be implemented in that way, but a simpler method is as follows: I = K * (1.8 - log(P + 2)); this is more or less correct in the case where the secondary missile is 20% the mass of the primary. Note that multiple stages are only efficient for P of 10 or lower. This approximation should only be used for vacuum missiles, as the changes in drag after the first stage is shed can be very important; if you want to build a multistage atmospheric rocket design it as a heavy missile with a payload of a lighter missile. Special rule: orbital missiles. By late TL 6, a multistage missile can reach orbit. In order to reach orbit, you must have a total impulse equal to 810 seconds (for the earth), plus enough to avoid hitting the ground (figure about 15%/(G-1)), plus enough to reach the desired altitude (usually about 1 second per 5 miles for low orbit, rather more complicated for high orbit; +335 seconds can reach escape velocity, or any orbit), plus enough to punch through the atmosphere (for a ground-based missile, figure 1000/(wt)^1/3 / (2+altitude in miles)). In addition, you can gain some impulse from the rotation of the earth (about 40 seconds for an easterly takeoff from cape canaveral), and a fighter- launched missile can add (speed/25) seconds. Thus, for example: TL 7 missile, 1 million lb(500 tons), launched east to LEO (100 miles) from cape canaveral at 3.5 Gs: I = 810 + 50 (gravity) + 20 (altitude) + 5(drag) - 40 (eastward) = 845; this is equal to 1.21*K, so we need a two-stage rocket, where 1.8-log(P+2) = 1.21. Thus, P+2=10^(0.59)=3.9, so P = 1.9, allowing our rocket to lift 9.5 tons. If we want a polar orbit, the loss of 40 seconds of free impulse drops this to 3.5 tons; similarly, a 1 ton rocket will suffer 40 seconds worth of drag, allowing it to lift about 8 lb... TL 7 fighter-based missile, 1000 lb, launching from 8 mile altitude at 1400 mph, east, at 6 Gs: I = 810 + 25(gravity) + 18(altitude) + 10(drag) - - 40 (direction) - 56 (speed) = 767 = 1.1*K. This is doable with a two-stage rocket, 1.8-log(P+2) = 1.1; thus, P = 3, allowing a 30 lb warhead.