On Becoming a Spacefaring Society Chapter One: Nuclear Propulsion If we are to become a true spacefaring society, we must abandon chemical rockets and focus our R&D on nuclear rockets. Ejner Fulsang efulsang@Comcast.net SAS -- 12OCT2017 1
NASA’s Three “Red - headed Step Children” of Manned Space Exploration 1) Failure to develop rocket technology beyond chemical rockets 2) Failure to compensate for zero-gee conditions in space 3) Failure to deal with high ambient radiation in space This presentation will address the first. 2
Who is the father of rocketry? 1) Some say the Chinese who invented gunpowder, the first solid rocket fuel. 2) Some say Robert Goddard, inventor of the liquid rocket, a vast improvement over the solid rocket. 3) Can’t forget Hermann Oberth who conceived of the multistage rocket that made it possible to launch heavy payloads to the moon with chemical rockets. 4) Most iconic is Wernher von Braun who gave us the Saturn V, the workhorse of the Apollo program. 5) But I say Konstantin Tsiolkovsky whose famous equation allowed us to apply the principles of rocketry to space flight. https://blog.sfgateway.com/index.php/the-founding-fathers-of-rocket-science/ 3
Konstantin Tsiolkovsky The Party Pooper of Space Travel (also the reason space travel is possible at all) Tsiolkovsky’s famous rocket equation: Delta V max = V e x ln (Wet Mass / Dry Mass) where: Delta-V max is the rocket’s maximum velocity, V e is the Exhaust Gas Velocity Wet Mass is the mass of the fueled rocket Dry Mass is the mass of the unfueled rocket Russian and Soviet rocket scientist Wet Mass / Dry Mass is called the Mass Ratio b 1857, d 1935 First, inevitably, the idea, the fantasy, the fairy tale. Then, scientific calculation. Ultimately, fulfillment crowns the dream. — Konstantin Tsiolkovsky http://www.projectrho.com/public_html/rocket/engines.php 4
What do we mean by Delta V max ? Here we have an astronaut floating in space. (He’s the rocket ship and the payload.) How fast is he going? We don’t know. We have no reference frame. Let’s assume his velocity V is zero. NOTE: velocity is a vector with speed and direction. If he doesn’t do anything, he will continue to sit payload at V = 0 , immobile, floating forever... boring. He needs a rocket motor! Mass = 500 kg With a rocket motor he can “do something!” He can change his velocity… Delta V . As long as he fires his rocket motor he will accelerate… until it runs out of fuel. At that point he will be at Delta V max . 5
Here we have two sophisticated NASA rocket motors from Home Depot*. One is empty. One is full of propellant. empty full Mass = 500 kg Mass = 9500 kg (Propellant is 9000 kg) 6 * Due to Congressional budget cuts
What do we mean by Wet Mass? = + Wet Mass Wet Mass = Mass = 500 kg Mass = 9500 kg 10,000 kg 7
What do we mean by Dry Mass? = + Dry Mass Dry Mass = Mass = 500 kg Mass = 500 kg 1000 kg 8
What do we mean by Mass Ratio? Wet Mass = 1000 = 10 10,000 Dry Mass 9
What is the astronaut’s Delta V max ? Assume for simplicity that exhaust gas velocity V e is 1 km/sec. Delta V max = V e x ln (Wet Mass / Dry Mass) Delta V max = 1 x ln (10) = 1 x 2.3 = 2.3 km/sec Why do we use ln (Wet Mass / Dry Mass)? Every time we pulse the rocket, we reduce the Wet Mass by shooting some propellant out the nozzle. Meanwhile, Dry Mass remains constant. Mass Ratio degrades until Wet Mass = Dry Mass. When you run out of propellant, your Mass Ratio = 1. 10
What if I want to go faster than 2.3 km/sec? Holding V e constant at 1.0 km/sec, I could increase the Mass Ratio by adding propellant. But this yields diminishing returns: 5.00 V e (km/s) Mass Ratio Delta V max (km/s) 4.50 1.5 0.41 4.00 Delta V max (km/s) 2 0.69 3.50 2.5 0.92 3.00 5 1.61 2.50 7.5 2.01 1.0 2.00 10 2.30 1.50 25 3.22 1.00 50 3.91 0.50 75 4.32 100 4.61 0.00 0 20 40 60 80 100 120 Mass Ratio Takeaway Message: If you start at the low end of the Mass Ratio scale, you get good returns for your fuel investment. But for Mass Ratios higher than 10, the payoff diminishes rapidly. 11
What if I want to go faster than 2.3 km/sec? Holding the Mass Ratio constant at 10 while increasing the exhaust gas velocity V e offers even returns: 250,000.0 V e (km/s) Delta V max (km/s) 200,000.0 Delta Vmax (km/s) 1 2.3 150,000.0 10 23.0 100 230.3 100,000.0 1,000 2,302.6 10,000 23,025.9 50,000.0 100,000 230,258.5 0.0 0 20,000 40,000 60,000 80,000 100,000 120,000 Exhaust Gas Velocity (V e ) Takeaway Message: Investing in rocket engine technology to increase V e is worth every penny! 12
Some practical thoughts about Delta V In theory, if you had a rocket that could achieve a Delta V max of 100 km/sec, you could actually reach a velocity of 100 km/sec. BUT then you have the problem of slowing down. Rocket ships don’t have brakes . In practice, you would use a portion of your Delta V budget to accelerate to your cruise speed, and then when you get close to your objective, you would do a flip-and-burn maneuver to slow down enough for orbit insertion. Of course, then you have the problem of returning home. And ideally, you would set aside a minimum 30% margin in your Delta V budget. So a typical round-trip mission profile would be as follows: Total Delta V 100 (%) Outbound Acceleration 17.5 Outbound Deceleration 17.5 Return Acceleration 17.5 Return Deceleration 17.5 Margin 30 13
How do chemical rockets fare with exhaust gas velocity? V e Thrust Propulsion Oxidizer/Fuel (km/sec) (Mega-Newtons) PBAN-APCP 2.6 24 Space Shuttle SRB x2 LOX/Kerosene 3.0 38.7 Saturn-V F-1 x5 LOX/Kerosene 2.6 7.6 SpaceX Merlin 1D x9 4.4 Space Shuttle RS-25 x3 LOX/LH2 5.4 One newton is 0.225 pounds of thrust The above rocket engines are weight lifters, designed to overcome atmospheric drag and earth’s gravity to place heavy payloads in Low Earth Orbit. NOTE: The highest possible V e for chemical rockets comes from LOX/LH2. Therefore, at V e = 4.4 km/sec and a Mass Ratio of 10, the best Delta V max you can hope for with a chemical rocket is 23 km/sec. This in turn means your best outbound leg velocity is ~4 km/sec. 14
Okay, you’re stuck with a chemical rocket and you want to go to Mars anyway… That would be economy class, aka the Hohmann Transfer Orbit*. Why do we call it a ‘transfer orbit?’ — Because we start out in Earth orbit (around the Sun) and we transfer to Mars orbit (around the Sun). Assume for simplicity that Earth and Mars orbits are circular. Mars at rendezvous Earth orbits the Sun at a distance of 1 AU at 29.79 km/sec. Mars orbits the Sun at a distance of 1.5 AU at 24.13 km/sec. (The farther from the Sun you are the slower your orbital velocity.) Pick a point opposite the Sun from Earth — that will be your rendezvous point. Wait for Mars to be ahead of Earth by Mars at launch 44.3 degrees — that will be your launch window, happens every 26 months. * http://www.projectrho.com/public_html/rocket/mission.php http://www.projectrho.com/public_html/rocket/mission.php#id--Hohmann_Transfer_Orbits 15
Okay, so you want to go to Mars… Initiate your launch from LEO, about 1000 km above Earth. Your burn will be enough to give you a 2.95 km/sec Delta V. After you reach that velocity shut down your engines and cruise. This will put you in an elliptical transfer orbit that is barely big enough to nick Mars’ orbit 2.5 AU away. As you approach Mars, your velocity will gradually degrade until you are only traveling 21.5 km/sec. If you do nothing else you will continue down the backside of the ellipse picking up speed as you go until you are back at your launch point traveling 33 km/sec again. BUT Earth won’t be there. We don’t want that, so we gun the engine when we reach Mars to add an extra 2.65 km/sec to our velocity to match Mars’ orbital velocity. This is sometimes called a circularization burn. 16
Okay, so you want to go to Mars… But we’re not quite done since we want to avoid crashing into Mars. For that we do an Orbit Insertion Burn to the tune of 3 km/sec which puts us in a stable Mars orbit at 500 km altitude. Altogether, your Hohmann transfer to Mars will cost you 9 km/sec of Delta V and will require 235 days travel time. Getting home is roughly the same except that you have to wait for planetary alignment before you light your rockets. That will be 516 days. Hopefully, you brought a book. The return leg is a little faster requiring only 191 days. Altogether, you’ll need 942 days. That’s a long time for vital equipment not to break, for crew not to get sick or injured, to not run out of essential stores (food, water, oxygen), and to not get cooked in interplanetary radiation (25 rems/year). https://www.quora.com/Why-is-it-important-that-on-the-launching-day-of-the-Mars-rover-the-two-planets-should-be-close-to-each-other 17
What if we want to get to Mars quicker? The Hohmann Transfer Orbit is a minimum sized ellipse that will just nick Mars’ orbit. So why not try a bigger ellipse? We initiate our elliptical transfer with a Delta V of 3.86 km/sec, but as we get close to Mars we have to do a much more aggressive braking burn of 6.23 km/sec. 18
What if we want to get to Mars even quicker still? We could abandon elliptical transfers altogether and go for a hyperbolic transfer . This one is a 93-day round trip with 17-day stay at Mars. 110 km/sec becomes 143 km/sec with 30% margin. 19 Dr. Nicola Sarzi-Amade, Global Aerospace Corporation, Irwindale, CA
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