Archive for the Science Category

Tsiolkovsky’s rocket equation

Posted in Intercept, Science with tags , , on December 28, 2012 by Mr Backman

I was fiddling with a TL-8 fission rocket design for going to the moon and back as cheap as possibly when I noticed something strange; going for more advanced materials would lower the mass of the ship and thus increasing its acceleration but it had no effect on delta-V? The design was for an upcoming article on landings, takeoffs, aerobraking, docking and ramming. It turned out to be just a bug and together with this post you can download the updated design spreadsheets, designs etc at the usual location.

Then I realised that the rules doesn’t dwell much on low tech rocket design, delta-V, mass ratios and such. These are the bread and butter of ‘real’ rocket design, and at the core of this rocket science art is the Tsiolkovsky’s rocket equation. Cool name for a post covering up my spreadsheet blunder and here we are.

Tsiolkovsky, Russian rocket pioneer and visionary did all the theoretical work for rocketry way before anyone really thought of rockets in space. He calculated the velocity needed to go to orbit and that to achieve it one should do it in a multi-stage rocket fueled by liquid Hydrogen and Oxygen, this was in 1903. Even before that, in 1896, he derived his famous rocket equation.

A real rocket accelerates by pushing stuff out the back, the faster it pushes and the heavier the stuff it pushes the higher the acceleration. Now, the tricky part is that as the rocket expends reaction mass it gets lighter which also increases acceleration. A rockets acceleration is at its lowest when it starts and at its highest just before it runs out of reaction mass. All this makes it hard to calculate just how much total velocity change a given rocket will have, twice the fuel will not give you twice the velocity change but more etc. Mr Tsiolkovsky helps us here with this simple formula:

Tsiolovsky rocket equaton

  • dV is the total change in velocity (m/s)
  • Vexh is the exhaust velocity (m/s)
  • M0 is the fully fueled mass of the ship (kg)
  • M1 is the empty mass after all fuel is gone (kg)

ln is the natural logarithm (logaritmus naturale) but you already knew that, right.
A derivation of the rocket equation and more facts about the great Konstantin Tsiolkovsky is available at Wikipedia.

So, whenever you design a ship with a fission or fusion rocket you now know how it gets its endurance value. Pay attention to the mass of components and if you can afford it you should try increasing the Material quality as this will reduce mass and increase acceleration Gs and endurance.

Whenever your friends complain about you fiddling with Intercept just tell them that you’re doing rocket science!

Air-raft to orbiting ship

Posted in Science, Traveller on December 29, 2010 by Mr Backman

Various canon Traveller sources state that Air-rafts can reach orbit and in my Traveller campaign precisely that situation arose during my weekend session with my kids. I assume here that the ship we want to match orbit with is in Low Earth Orbit (LEO). The problem is much simpler if the ship is hovering on its contragrav above the planet but that is not what the canon sources say; ‘orbit’ does not mean outside the atmosphere, it means outside the atmosphere with enough speed for centripetal forces to match gravity.

If you dig into the problem there are lots of complications that crop up:

Problems with the air-raft
An open topped vehicle is hardly built for vacuum as this costs a lot extra, so I guess the instrumentation, upholstery etc will break in vacuum. Another problem is that an air-raft produces something like 0.1 G thrust for propulsion which mean (ballpark calculations here) that to reach say 5 km/s orbital velocity they must accelerate for over an hour (ca 5000 seconds).

Problems with the calculations
To match the orbit of a ship the air-raft driver must eyeball the ship and vector (yes, LEO ships can be seen at dusk or dawn by the human eye) and then match that orbit by hand with the air-raft over a more than an hour long acceleration phase. The air-raft will have no instrumentation for orbit matching and the like, just an accelerometer based (Traveller vehicles does not rely on the crude GPS system we use) absolute positional instrument that also indicate height as well as speed gauges. Calculating the orbital mechanics and driving the air-raft to comply is in my opinion a really hard problem for a spaceship pilot and impossible for mere grav-jockeys. If you think orbit matching is a piece of cake try it yourself with the free PC space simulator Orbiter.

IMTU (In My Traveller Universe)
My TL progression differs from canon and GURPS Traveller and this causes even more problems:
(I don’t add gravtech until TL 10, so I can have cultures with jumpdrives without grav and floorfield, ‘Hard-SF with jump’ if you will)
Jumpdrives TL 9
Floaters TL 10
Floorfield TL 11
Gravthrust TL 12
Floater gravbelts TL 13
Reactionless drives TL 13
Gravbelts TL 14
Tractor beams TL 15
Pressor beams TL 16
Rattlers (high freq tractor weapons) TL 17

Floaters are grav ‘thrusters’ that can only negate gravity, they can never create upwards or lateral thrust, just negate the downward pull of gravity. Floaters and gravthrust have ‘thrust’ proportional to local gravity so a 1G (Thrust = mass) floater will negate gravity on all planets, regardless of gravitation (simplifies designing gravvehícles and ‘explains’ why gravthrust is useless for interplanetary travel). Floaters come at TL 10, are much cheaper and require much less power per ‘thrust’ than regular gravthrust. Regular gravthrusters produce floating at the cost of x1/10 thrust (a 1G gravthrust would use 0.1 G for floating and 0.9 G for propulsion for example).
My air-rafts are so cheap they use floaters powered by a fuelcell for lift and turbojet for thrust (both the fuelcell and turbojet are hydrogen powered and need an atmosphere with oxygen to work).

So IMTU the air-rafts cannot reach orbit at all, they cannot even operate in anything near vacuum, fitted with compressors they can work in Very thin atmospheres, but that’s it.

Edit: I have updated the Intercept design system to reflect the TL progression (and no, there are no tractor, pressor or rattlers yet).

100 diameters limit

Posted in Rules, Science, Science fiction, Traveller on May 30, 2010 by Mr Backman

Traveller has always had the rule that hyperspace jumps should be made beyond 100 diameters of the planet, gasgiant, ship, star or nearby massive object. When some kind of reason for this is mentioned it goes along the lines of  ‘too deep within the gravity well’ or other reference to gravity. Can ships jump inside nebulae (they’d certainly be inside 100 diameters of the nebula)? How can ships jump at all when they are always inside 100 diameters of the milky way galaxy? What about jumping near black holes or neutron stars (shouldn’t the density of objects be accounted for at all)?

We all know the real reason is to force ships to actually travel in space before jumping, without such a limit the ships could just as well jump directly from the ground and not much space travelling would occur. So let us all agree that wa want some kind of rule that forces ships to fly away from planets before jumping, preferrable such a rule should behave as the 100 diameter rule for planets yet still make some scientific sense. The rule should also dismiss the cases of nebulae and galaxies so ships can jump inside these while still abiding to the rule. If the rule is based on gravity instead of some weird new invented force all the better.

Gravity then, is proportional to the mass of the object and inversely proportional to the square of the distance. Gravitational force is not the only measure of gravity, we have gravitational potential and tidal force as well. These two are effects derived out of gravity but they behave differently range wise:

  • Gravitational potential falls off as M/R, where M is the mass of the planet and R is the distance from the planet. It is a measure of the energy needed to reach the distance R.
  • Gravitational acceleration falls off as M/R^2, where M is the mass of the planet and R is the distance from the planet. It is a measure of the gravitational acceleration exerted on an object at the distance R.
  • Gravitational tidal force falls off as  M/R^3, where M is the mass of the planet and R is the distance from the planet. It measures the fall-off rate of gravitational acceleration. It is the force that causes ebb and flood on Earth as well as what causes the moon to always show the same face towards Earth.

The mass of a planet is proportional to its volume (given the same density), that means that it rises with D^3. Twice the diameter and the planet becomes 2^3 = 8 times as massive. The 100 diameter rules states that a planet twice as large must be jumped from twice as far away and as mass scales with D^3 we need something that scales as 1/R^3 and the only gravity effect that fit the bill is tidal force. Using tidal force as a limiter for when a safe jump can be performed makes a lot of sense; it is a measure of fast gravity changes near the ship. If jumdrives need a uniform gravity field to work properly the tidal force tells us how much gravity differs in different parts of the ship. If jumpdrives need to know the exact gravity pull when jumping the tidal force tell us how much error we get from our positional error. 

Safe jump distance (taught to Imperial school children to be 100 x the diameter of the object) is really calculated like this (x^(1/3) means the cubic root of x):

  • Planet safe jump Rj = 1 000 000 km x (Traveller Size / 8 ), multiply by the cube root of Earth density if you want that level of detail (Earth has density 1.0)
  • Planet safe jump Rj = 1 000 000 km x (M) ^(1/3), M is measured in Earth masses (Earth has a mass of 1.0)
  • Star safe jump Rj = 0.5 AU x (M) ^(1/3), M is the stars mass in Solar masses (Sol has a mass of 1.0)

What does all this give us? The referee can tell its players that they must travel out 100 diameters from a planet to “where the tidal force is weak enough to safely engage the jump drive”. If one wants the detail one can calculate the actual safe jump distance from any object. When scientifically versed players asked how one can jump inside the 100 diameters of the milky way the referee can tell them it is because the tidal force from the galactic centre is way too weak to cause any problems, the same goes for jumping inside nebulae.

Note: I have taken the liberty to round off figures in the formulae above, it should really be 1 280 000 km but I find one million kilometers easier to remember.

Relativistic rock? Is that a sub-genre of Space rock? You know, Hawkwind, Ufomammut and the like?

The emptiness of space

Posted in Boardgames, Computer games, Films and TV, Science, Science fiction, Uncategorized on April 2, 2010 by Mr Backman

The Atomic rocket website deal with realistic space flight and combat in the most exhaustive manner possible. You can get tons of information on just about everything dealing with realistic spaceflight there and I consider it the best website on the net! There are however some assumptions they make which lead to the conclusion that space battles will have no ambushes, no role for stealth or sensors and little tactical decisions. The assumption is that space is empty and any approaching ship will be detected well before it come in harm’s way. There is no preferred direction in deep space so a space battles involving two ships could just as well be fought in one dimension, range only.

In air to air combat the two horizontal dimensions work the same but the vertical dimension works differently: The highest planes can dive for speed, lower planes run the risk of hitting the ground. As air pressure diminish with altitude each plane has ceilings above which they can no longer fly. Ship to ship combat in the age of sail had the weather gauge which gave the upwind ship advantages over the downwind ones and if the ships were close to shore there was also the consideration of how deep water each ship required to avoid running aground.

But space IS empty and equal in all directions so space battles WILL be predictable and leave no room for maneuver you may say, or you could grow pointy ears and say that space is filled with nebulae, dense asteroid fields, mysterious energy fields etc which give ample opportunity for ambushes, stealth and tactical maneuvering. I believe that we don’t need to go all Space Fantasy to have interesting space battles if we only change the our assumptions a little about where the battles take place.

In Traveller, the rpg I originally wrote Intercept for, ships use jump drives to travel between planets, you fly 100 planetary diameters away, jump to the next starsystem and fly the 100 planetary diameters to land or orbit. All space battles would take place near a planet or gas giant, more rarely near single asteroids or comets. Planets are huge, even as space combat ranges go and gas giants are even larger. If a ship is on the other side of a planet you have no way of knowing how it changes its vector, regardless of the amount of heat and light from its drive. When two ships moves so they have line of sight which each other again the ship that shoots first will certainly hit the other and probably take it out. The commander that is better at outguessing his opponent will spot him first and can get off the first shot, simply because surveying the sky takes time so where you start scanning is crucial. Ships in planetary shadow will be as dark as space itself and only visible on infrared. Ships near the direction of the Sun will be harder to spot, their weak signature drowning in the huge outpouring from the sun. The excellent Rocketpunk Manifesto website has an interesting article that also question the assumption that space battles will and should be fought in deep space.

All this allow us to make somewhat realistic space battles where ambushes are possible, maneuvering matter and sensors vs stealth plays a part, only if we assume that battles will take place near planets instead of in deep space. When we design space combat board games, computer games, books etc we should take planets, sun direction etc into account to make space battles more realistic while keeping the fun. Star Trek and other space fantasies are cop-outs, and there is no excuse to go there for whatever reason.