Don't Forget Blast-off
On This Page
The spacecraft's acceleration depends on the total thrust and the spacecraft's mass. For most purposes, we don't care about this. The spacecraft can be theoretically any size. The equation is
A = F / Mi
- A = spacecraft's acceleration (m/s), divide by 9.81 for Gs
- F = spacecraft's thrust (newtons)
- Mi = spacecraft's current mass (kg)
If the Arcturus can manage 19,620,000 newtons of thrust and masses 200,000 kg, 19,620,000 / 200,000 = 98.1 m/s or 10 gs of acceleration.
As a short cut, you can calculate acceleration using the Transit Time Nomogram
We don't care about acceleration, with the major exception of landing and take-off. If the Polaris is taking off from Terra, and it does not produce acceleration greater than 1 g, it is just going to hover there vibrating while the jet burns a hole in the ground. For these calculations, for Mi use the spacecraft's mass with full propellant tanks. As a rule of thumb, you want the spacecraft capable of doing 1.5 g, though 1.3 g will do in theory, and 10.0 g will really reduce the gravitational drag. 1.5 g = 14.72 m/s. The value you pick will be what you will use to calculate Apg in the gravitational drag formula.
On the Transit Time Nomogram, the minimum liftoff values are labeled on the Acceleration scale for your convenience. In the example above, a 46 metric ton spacecraft with a particle-bed nuclear thermal propulsion system can accelerate at 0.5 g. Glancing at the chart, you can see that the spacecraft has no trouble lifting off from Mercury, Mars, and the various moons; but cannot lift off from Venus or Earth.
This means that the engine's so-called "thrust to weight ratio" has to be higher than 1.0 if the rocket is expected to take off from Terra. (You can get away with less on smaller planets. Maybe.) Sometimes you are lucky and can find this value while researching propulsion systems. Lucky you, I included this data in the engine table above. Bottom line: do not use any engine marked "no" in the T/W>1.0 column if the spacecraft has to be capable of takeoff or landing.
At this website, they suggest that the optimum thrust to weight ratio varies from 1.15 to 1.2.
Gross Lift Off Weight
By rearranging the equation for acceleration, given the ship's thrust we can calculate the maximum mass of the ship with full propellant tanks (the mass of the ship with full tanks is often called Gross Lift Off Weight or GLOW).
GLOW(kg) = Thrust(newtons) / accel(m/s)
GLOW(kg) = Thrust(newtons) / 14.72(m/s)
A single Gas Core engine has a thrust of 3,500,000 newtons. If Polaris has one GC engine, its maximum liftoff mass is 237.8 tons, which is pretty disappointing. ( 3,500,000 / 14.72 = 237,771 kg )
But if it had five GC engines, it would have a liftoff mass of 1188.9 tons. That's more like it.
This also can be calculated with the Transit Time Nomogram
The other major exception is that a ship's acceleration affect maneuverability. This is important if somebody is shooting at you. It is hard to jink when your acceleration is measured in humming-bird powers.
Note that adding more engines only increases the acceleration and thrust (and the rate of propellant consumption). It does nothing to the deltaV or exhaust velocity. It also cuts into the payload mass. Also note that if an engine has a thrust to weight ratio below one, it doesn't matter how many of them you add, it still won't be able to lift-off.
Multiple engines produce other problems that have to be taken into account. If they are too close together, they inflict their waste heat on each other, increasing the heat radiator requirements. If they are too far apart and are of a type that emits nuclear radiation, they increase the number of shadow shields required, which cuts into the payload.
Think of the Earth as being at the bottom of a funnel-shaped well whose walls become less steep as you climb away from Earth. (ed note: the "gravity well")
Paint the walls of the funnel in zones of different colors to represent the various space traffic control center jurisdictions. The ones nearest Earth at the bottom of the funnel are controlled from national centers that are, you hope, in communication with one another and swapping data. The ones farther out are watched by seven other centers located in GEO. And the ones in the nearly-flat upper part of the funnel are four in number centered on L-4, the Moon, L-5, and a huge "uncontrolled sector" stretching around lunar orbit from 30-degrees ahead of L-4 to 30-degrees behind L-5 where there wasn't anything then.
Now spin the funnel so the bottom part representing a distance up to 50,000 kilometers goes around once in 24 hours. Spin the top part from 50,000 kilometers altitude out to a half-million kilometers at the lunar rate of 29.5 days.
Located on the walls of this madly turning mult-colored funnel are marbles spinning around its surface fast enough so they don't fall down the funnel. Some of them are deadly marbles; come close enough and you'll burn. Others are big and fragile, but massive enough to destroy your ship if you hit one. Still others are ships like your own, plying space for fun, profit, or military purposes. An unknown number of the last are capable of whanging you with various and sundry weapons.
Your mission: without coming afoul of any of this, get to the flat tableland on top, then locate and dock to a group of fly-specks called L-5.
Try it on your computer. Good luck.