> -----Original Message----- > From: [email protected] [mailto:gurpsnet-l- > [email protected]] On Behalf Of Onno Meyer > Sent: Tuesday, April 23, 2013 12:09 PM > To: [email protected] > Subject: [gurps] Skycarrier Operations > > Still playing with the numbers ... > > Say I have a 20,000-ton aircraft with a 1,800,000-cf body and two > 100,000-cf wings. If I made no math errors, the Expansion > 2 rules give a stall speed of about 380 mph.
Let's see. I have some actual aerodynamics code floating around. Base wing area is 13,000 sf (wings are x2 area? I haven't looked at VE2 in ages), base body area is 90,000 sf (30% efficiency as lifting body iirc?), so its lift area by VE2 logic is 79,000 square feet. We'll call that a planform area of 3,670 m^2. L = 1/2 * rho * v^2 * A * Cl. L is the weight of the aircraft, 180 million newtons. Rho is atmospheric density; 1.225 kg/m^3 at sea level. V is true airspeed; we'll work this out later. A is planform area, 3,670 m^2 Cl is coefficient of lift; it depends on attack angles but typically has a maximum of about 1.5. Thus, L = 2,246 kg/m * Cl * v^2. To fly, Cl*v^2 must be at least 80,142. If we set Cl to 1.5 and v to 232 m/s, we get a total of 80,736, so this is our stall speed at sea level (about 520 mph). During takeoff we benefit from ground effect; if that doubles lift, that drops stall to 364 mph. I suspect Vxii is assuming ground effect in its stall speed. Now, for work to stay at this speed: Induced Drag = Lift^2/(0.5 * rho * v^2 * (wing area) * pi * (Oswald efficiency) * (aspect ratio)). Because much of the lift area comes from the carrier body, it's likely that both efficiency and aspect ratio will be fairly low; we'll go with 0.85 and 6 (150 meter wingspan). Thus, Di = (1.8e8)^2 / (0.5 * 1.225 * 232^2 * 3670 * 3.1416 * 0.85 * 6) = ~17 million newtons. Parasitic Drag = 0.5 * rho * v^2 * Cd * A. VE2 does not give us good tools for working out Cd*A, and the streamlining rules seem to confuse two different meanings for Cd (for most objects, Cd is drag / (frontal cross-section); for aircraft, Cd is drag / (wing area). These two are not directly comparable), but a plausible figure is something like 200 m^2. Thus: Dp = 0.5 * 1.225 * 232^2 * 200 = ~6.6 million newtons. Total 23.6 million newtons. Now, you might notice that Di goes down with velocity, while Dp goes up. Unfortunately, we're already pretty close to mach 1, and at high altitudes we'll be closer (multiply stall speed by the -1/2 power of air density relative to sea level air density) so not a lot of room for improvement. We're basically pushing on air, so power requirement is Drag * Velocity / Rotor Efficiency or about 5.5 gigawatts, which is less than its hover power requirements but not exactly trivial.
_______________________________________________ GurpsNet-L mailing list <[email protected]> http://mail.sjgames.com/mailman/listinfo/gurpsnet-l
