Gaseous planetary environments (Mars, Venus, Titan) Lighter-than- air (balloons, dirigibles) Heavier-than- air (aircraft, rotorcraft) 1 2018 David L. Akin - All rights reserved http://spacecraft.ssl.umd.edu
Atmospheric Density with Altitude Pressure=the integral of the atmospheric density in the column above the reference area = f(h) P o = Z 1 o gdh = o g Z 1 o e h hs dh = o gh s he h hs = o gh s [0 1] i 1 o Earth: o = 1.226 kg m 3 ; h s = 7524m; P o = o gh s P o (calc) = 90, 400 Pa; P o (act) = 101, 300 Pa o, P o 2
Exponential Atmospheres = o e h/h s o =Referencedensity h s = Scale height 3
Planetary Entry - Physical Data Radius (km) µ o (km 3 /sec 2 ) (kg/m 3 ) hs (km) vesc (km/sec) Earth 6378 398,604 1.225 7.524 11.18 Mars 3393 42,840 0.0993 27.7 5.025 Venus 6052 325,600 16.02 6.227 10.37 Titan 2575 8969 5.474 23.93 2.639 4
Comparison of Planetary Atmospheres 100 Atmospheric Density (kg/m3) 1 0.01 1E-04 1E-06 1E-08 1E-10 1E-12 1E-14 1E-16 1E-18 1E-20 0 50 100 150 200 250 300 Altitude (km) Earth Mars Venus 5
Atmospheric Neutral Buoyancy Given an enclosed volume V of gas with density ρ Lift force is V(ρ atm -ρ) - must be mg on Earth ~1 kg lift/cubic meter of He on Mars ~10 gms lift/cubic meter of He Horizontal velocity at equilibrium is identical to wind speed Interior pressure generally identical to ambient (except for superpressure balloons) Can generate low density through choice of gas, heating 6
Buoyancy by Light Gases Ideal gas law Given same volume and temperature, gas densities scale proportionally to molecular weight n Mars atmosphere is essentially CO 2 He: H 2 : PV = nrt n = 44 n = 4; = 90.3 gm/m 3 n = 2; = 94.8 gm/m 3 Hindenburg airship would have a total lift capacity of 49,894 kg in Mars atmosphere and gravity (Earth lift capacity 232,000 kg - factor of 4.6) 7
Goodyear Blimp Volume 5380 m 3 Empty mass 4252 kg Gross mass 5824 kg Mars lift 1278 kg 8
Thermal Balloons ( Montgolfieres ) Use ambient gases and thermal difference to create lift Ideal gas gas density inversely proportional to temperature Ambient atmospheric temperature on Mars ~200K Heat gases to 300K: lift force 33 gm/m 3 (about 1/3 of He or H 2 balloon) 9
Dual-Lift Mars Balloon Concept Heinsheimer, Friend, and Siegel, TITAN Systems (http://home.earthlink.net/~rcfriend/mars-33.htm) 10
Data Collection by Dragging Heinsheimer, Friend, and Siegel, Concepts for Autonomous Flight Control for a Balloon on Mars NASA 89N15600 11
Superpressure Balloons Interior pressure greater than external ambient Envelope is relatively insensitive (in terms of volume) to interior pressure changes Diurnal temperature changes have minimal effect on lift Provides stable long-term platform for extended flights Envelope must be significantly stronger (and therefore heavier) than ambient-pressure balloons 12
Flight Missions with Balloons Venus: Vega - Russian Vega missions put two French balloons in Venus atmosphere in 1985 One died in 56 minutes One operated for two days (battery limitations) Mars: French dual-balloon system (solar thermal balloon tied to He/H 2 balloon - gas balloon keeps solar balloon off the ground, thermal balloon lifts payloads when sun warms envelope) -never flew 13
Future Concepts Titan Aerover 14
Heavier than Atmosphere Approaches Fixed wing Gliders Powered Propellers Jet Rocket Rotary wing Hybrid/Reconfigurable 15
Dynamic Atmospheric Lift Drag Lift Thrust D = 1 2 v2 Sc D Weight L = 1 2 v2 Sc L For steady, level flight: T = D W = L = D L D = T L D L = 1 2 v2 Sc D L 16 D L = W = mg T = W L/D
Atmospheric Flight Performance L = 1 2 v2 Sc L D = 1 2 v2 Sc D from Anderson, Introduction to Flight, Third Edition McGraw Hill, 1989 c D = c Do + c Di = c Do + c2 L e(ar) 17
Aspect Ratio Wing area S Aspect ratio AR = b2 S Oswald e ciency factor e 0.9 18
Lift Curve from Anderson, Introduction to Flight, Third Edition McGraw Hill, 1989 19
Mars Atmosphere =0.020 kg m 3 T = 210 K g =3.71 R = 188.92 m sec 2 =1.2941 J kg K Speed of sound a = p RT = 226.6 m sec 20
Aircraft Flight Performance v stall = U-2 high-altitude spy plane Cruises at 70,000+ feet m=18,000 kg b=32 m S~64 m 2 s mg S U-2 v stall(mars) = 228.4 m sec 2 2 c L(max) 21
Stable Gliding Flight Flight path angle D = mg sin mg = W = L =) sin = 1 22 L/D High performance glider L/D 30 Deploy at 10 km V 200 m sec =) Range 300 km =) Flight time 25 min
Powered Flight T = ṁ(v e V ) v e = Exhaust velocity; V = Flight velocity Power into flow P f = ṁ 2 v2 e V 2 Power into flight P v = TV Propulsive e ciency prop = 2 1+ v e V 23
Power Required Powered required P R = T R V Thrust required T R = W c L /c s D L = W = 1 2 V 2 2W Sc L V = Sc L s P R = W 2W c L /c D Sc L s 2W P R = 3 c 2 D 1 Sc 3 _ L c 3/2 /c D 24 L
Power Required with Velocity from Anderson, Introduction to Flight, Third Edition McGraw Hill, 1989 25
Minimum Power and Thrust from Anderson, Introduction to Flight, Third Edition McGraw Hill, 1989 26
Effect of Altitude on Power from Anderson, Introduction to Flight, Third Edition McGraw Hill, 1989 27
Actuator Disk Size Engine intake area A ṁ = AV T = D = T = ṁv = AV (v e V ) W L/D AV (v e V )= W L/D W A = (L/D) V (v e V ) 28
Mars Helicopter (Mars 2020) 29
Rotorcraft (Quick and Dirty) Thrust is downwards Hovering flight T=W Power calculations same as before if L/D=1 Incline lift vector angle W = T cos 30 from vertical =) T = mg cos D = T sin =) D = mg tan s 1 2 V 2 2mg tan Sc D = mg tan =) V = Sc D
Looking for Equation for Range E ciency = propulsive power fuel power = Tv e ṁ f h h heating value of fuel overall = Tv e ṁ f h dw dt = ṁ f g = L D W T ṁ f g dw dt = Wv e h g L D Tv e ṁ f h = h g L D Wv e overall 31
More Aerial Range Rewrite and integrate dw W = v e dt = ln W = C h L overall g D h g L D v e t overall Initial conditions - at t =0W = W init C = ln W init Range = h g Range = L D overall ln W init V L D gsfc ln W init W final W final -->Breguet Range Equation 32
Some Notes on Breguet Range Eqn SFC Specific Fuel Consumption For propeller-driven aircraft, For jet aircraft, SFC = SFC = mass of fuel (power)(time) mass of fuel (thrust)(time) = ṁ T So SFC = 1 (in appropriate units) I sp 33
Breguet Endurance Equations For propeller-driven aircraft, E = SFC For jet aircraft, c 3/2 L c D p 2 S 1 p mf 1 p mo E = 1 SFC c L c D ln m o m f 34