Step 5 - Locomotion

Ground Vehicles
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Water Craft
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Aircraft
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Spacecraft

MHD Thrusters

Any MHD turbine can have thrusters fitted for launching from a planet's surface into orbit. This adds 10% of to the volume and mass of the power plant and 20% to the cost.

I did some research into the thrusters as listed in the Naval Architect's Manual and discovered that they are consistent with current projections on advanced rocket engines. Here's the result of my research -

To start with, let's look at the question of the Specific Impulse, or I_sp. NASA's glossaries define specific impulse as the thrust ( force in Newtons ) obtained from each unit mass of propellant ( kg of fuel and oxidiser ), consumed in 1 second. Things can get a little hairy here with this definition, as the units of I_sp are normally quoted as seconds ; this is only true if the unit weight of propellant is used ( for reasons I won't go into here - if the reader is interested there's a good discussion of the subject on NASA's website ).

Anyhow, we will take I_sp in seconds. Here are some typical values for I_sp for contemporary fuel-oxidisers -

The Space Shuttle Solid Rocket Boosters have a Specific Impulse of about 240 s, while the Main Engine varies from 363 s at sea level to 455 s in vacuum. That last variation is worth noting - rockets are often less effective in an atmosphere. However, we will ignore this effect ( called "pressure thrust" ) for the purposes of this document.

According to the Naval Architect's Manual, the required mass of fuel for one trip to orbit is one sixth of the total mass excluding this fuel. This means that the initial "pre-launch" mass to "all-burnt" mass ratio is 7:6.

A simple relationship exists between these two masses, the specific impulse and the velocity of the rocket at "all-burnt". This is

ln( M_L/ M_B ) = C_B / I_spg

where M_L is the launch mass, M_B is the all-burnt mass, C_B is the rocket velocity in metres per second at all burnt, I_sp is the specific impulse in seconds and g is the acceleration due to gravity at launch in metres per second per second.

Given that we have a M_L: M_B ratio of 7:6, the left hand side becomes the natural log of 7/6 or about 0.154. For a final velocity of 11125 m s^-1 ( escape velocity for the Earth ) and an acceleration due to gravity of 9.8 m s^-2, we get a Specific Impulse of 7364 seconds. This is nearly 16 times the performance of the Space Shuttle Main Engine in vacuum !

Since MHD thrusters are predicted to have specific impulses of 3000-4000 by NASA, we are in the right order of magnitude, just more efficient. I think that the specific impulse figure makes sense as a result.

Rocket thrust is given by the formula -

T = ( m / g )C

where T is thrust in Newtons, m is the mass of propellant spent per second ( or the "mass flow rate" ) in kg, g is the force exerted by gravity ( 9.8 Newtons for Earth ) and C is the velocity of the exhaust in metres per second ( and not the speed of light ! )

Since the specific impulse is equal to T/m, we can determine that the exhaust velocity must be the specific impulse times the force exerted by gravity. For our MHD thruster, this gives an exhaust velocity of about 72,170 metres per second ! That's 72 kilometres per second, or an amazing 212 times the speed of sound at sea level. This will not be quiet !

Ion Drives
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Solar Sails

Solar sails use the impact of photons on a large reflecting surface to produce thrust. They are governed by the formulae a = 2P/mc where a is the imparted acceleration in m s^-2, P is the power in watts per square metre received from the local star multiplied by the sail area ( see solar panels to calculate P ), m is the mass of the entire vessel in kg and c is the speed of light in metres per second ( 3x10⁸m s^-1 ).

Solar sails are very thin, in the order of 0.2 microns ( 1x10^-7 metres, or about 1000 atoms thick ). They consist of a layer of aluminium, vacuum deposited on a plastic substrate. This has a mass of about 5.4 grams per square metre. We shall use a value of 8 grams per square metre, once the supporting structures, "ripstops" in the sail and necessary electrical shorting mechanisms have been accounted for.

A solar sail therefore has the following characteristics, which you can use a guideline for constructing your own sails -

0.001 m s^-2 might not sound very much, but it amounts to 86.4 metres per second over a single day.

Chemical Rocket Propulsion
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Starships

Stutterwarp Drives

The Jerome Effect Drive, or Stutterwarp, is the only "exception" to the laws of physics postulated by 2300AD. I have derived some formulae for the mass, volume and cost of Stutterwarp drives based on the tables in the Naval Architects' Manual, which are presented below.

where "p" in the volume column is the cube root of the drive input power in megawatts.

I have extrapolated the following Stutterwarp efficiencies from the tables in the Naval Architects' Manual for the new technology levels in these Design Sequences.

This page was last updated on the 10^th July 1997.

This page is © 1997 Andy Brick except where components are already copyright / trademarked by others in which case their use is not intended as a challenge to such ownership.