Archive for the Science Category

Vector movement game units



Plotting example



Some examples:






The two formulas are:

Formula one and two



Formuila one with prior speed


Formula and area


Formula graph


  • Turn 1: 1 triangle plus 0 rectangles = 0.5
  • Turn 2: 2 triangles plus 1 rectangle = 2.0
  • Turn 3: 3 triangles plus 3 rectangles = 4.5
  • Turn 4: 4 triangles plus 6 rectangles = 8.0

and so forth…





Units for formula (1)

  • A = 10 m/s^2
  • T = 1000 s
  • S = 5000 km

Distance earth – moon will be 76 squares.

Traveling 76 squares with 1 unit acceleration will be


Units for formula (2)

  • A = 10 m/s^2
  • T = 1000 s
  • S = 5000 km

Distance earth – moon will be 38 squares.





Apollo 11 50 years anniversary July 16 1969




Sensor types part 1

Posted in Intercept, Rules, Science on September 20, 2018 by Anders Backman

Planet LOS in Star Wars

Space combat takes place at incredible ranges, tens of thousands of kilometers, and unlike in the movies, you won’t see anything through your window; a nuclear detonation for sure, fission or fusion thrusters as pinpoints of light maybe, the plume of a missile just before it hits you, the blinding flash from a laser hitting your ship, but aside from that nothing…

All ships carry sensors to see things around them and this is especially true of warships. All ships will have optical sensors seeing in visual and infrared wavelengths and most will also have radar. More exotic sensors such as neutrino or gravity sensors may be carried by larger or more specialized vessels.

Visual, infrared and radar sensors are mounted on the surface of the hull and can only be used when unfolded and extended, popped out as it is called in the game. Neutrino and mass sensors sees right through the hull so they can be used whether popped out or not. This make them especially suitable for military purposes as they can be used while still protected by the ships armor.


Visual scans are done with optical telescopes collecting light from visible wavelengths.

Light sources can be light from the sun reflected from the hull. How much depends on the strength of the sunlight, the area of the reflecting hull and how reflective the hull material is.

Light can also be directly emitted by a ships thrust, either the intense light from fission or fusion rocket plumes or the much fainter glow from impulse thrusters or floaters (that magic sci-fi blue glow).

The Inverse square law

The light falls off in strength as it spreads from its source, in both dimensions, if range doubles the intensity goes down as 1/2 times 1/2 or 1/4.


Popular media usually depict space as cold but in reality the problem is the opposite, getting rid of heat is hard part and the only viable long term way of doing it is by radiating it away. Every object radiates heat, how much depends on its temperature.

Ships have optical sensors that can either look in visual wavelengths or in infrared to detect objects as they radiate heat to cool. Ships radiate enormous amounts of heat when using fission or fusion thrusters, less infrared is radiated from the power plant when running, ships also radiate a faint heat from the temperature of the hull itself.

The infrared light falls off the same way as visual light, by the square of the distance. A given ship is typically easier to detect visually than by infrared, at least when the ship is in sunlight or if the ship has a running power plant. If the ship is using fission or fusion thrusters it’s about as easy regardless of using infrared or visual scanning. What to use really depends on what you think you are trying to find, tricky.

Plotting board


Everyone is familiar with radar works; you send out radio bursts that bounce off the target and get detected as it comes back.

One problem with radar is that it falls off much faster than visual or infrared does. Radar, although invented during World War II didn’t detect the planet Venus until 1961 yet it can easily be seen by the naked eye. Doesn’t radar waves fall off by the inverse square as visual and infrared does?

Of course they do. The problem is they fall off by the inverse square both going there and coming back again, 1/r^2 going there x 1/r^2 coming back again or, 1/r^4. If this sound weird and hard to grasp think about the following analogy:

You walk at night in a forest with a flashlight in your hand. The flashlight is a powerful maglite showing you the trees out to about 30 meters.

The flashlights range depends on the power of the flashlight but also the quality and focus of the lights parabolic mirror. The light falls off going out, bounces off trees and falls off coming back again, back to your eyes, your detectors, just like a radar.

Let’s say you decide to try your car lights instead. They must be a hundred times more powerful right? And now you can see trees out to about a hundred meters, three times farther or so. Three to the fourth power (3^4) is about a hundred (81) so that terrible range fall off of radar affects flashlights and headlights the same way.


Two men in a rubber raft inspect the wall of photodetectors
of the partly filled Super-Kamiokande neutrino detector (Ars Technica)


Neutrinos are these strange subatomic ghost particles created in fission and fusion reactions. These particles really fleeting, reacting to next to nothing. Build a wall one lightyear thick and half of them still get through. How can one ever hope to detect them with something smaller than a solar system, smaller than a planet even, small enough to fit on a ship?

What you do is you amass an enormous amount of atoms, in the hope that one neutrino might interact with one of them and then surround the mass with super sensitive detectors hoping to catch that one interaction somehow. The first detectors used thousands of cubic meters of water or chlorine as the mass and after waiting a long time they got the first signal from the sun. Imagine that, it took this enormous tank lined with super sensitive detectors sitting for months to detect a single neutrino coming from this enormous fusion reactor we call the sun.

Neutrino detectors in Intercept appear at TL-11 and assumes that some breakthrough has appeared, some resonance to exploit or some other way to make the neutrino detectors much smaller and much more sensitive, still bulky but practical. Neutrinos created in fission or fusion thrusters and fission or fusion power plants are what these detectors see. As the neutrinos leave their source they spread out, just as the visible photons for the visual scans and the infrared photons for the IR scans so the fall off is the same.

Neutrino sensors can only detect fission and fusion thrusters and fission and fusion power plants. On the other hand when they can see targets on planets or right through planets as if they aren’t there at all. In fact, a ship in the planetary shadow scanning towards the sun will be affected by Sunglare as if the planet wasn’t there at all.

Gravity with Thrust


Detecting a nearby mass seems easy. Just measure its gravitational pull on you. Not so easy. Imagine you were locked inside a small box either being a hundred km above earth and falling towards it (let’s ignore air drag completely) or being a light year away in the depth of space.

How can you detect which is case it is? How can you detect how far away earth is and in what direction? In both cases the box and you would be at rest with each other, either falling freely towards earth or just drifting in interstellar space. You could peek out of the box but that would be cheating. There is one difference that you can actually measure, being near earth means you closest point, say your toe, would be pulled towards earth a tiny amount more than your furthest point, say your nose, the difference between these pulls could be measured as a very weak force and this force would grow weaker the farther away from earth you go, a light year away in deep space and you’d measure nothing at all.

This force is called the tidal force and pulls apart parts of objects in a gravity field. The ocean water closest to the moon gets pulled towards the moon relative the water on the other side causing two bulges that move as the earth rotates. Yes that is why there are two tides each 24 hours.

Tidal force falls off as 1/r^3, double the range and the tidal force is 1/2 x 1/2 x 1/2 or 1/8 the strength. This limits the range of mass sensors but on the other hand they can see right through planets and because of the 1/r^3 falloff can scan towards the sun.

Mass sensors detect the mass of a ship directly but usually they detect the much stronger emissions from the gravitic Impulse or Floaters and also any working floorfields. This means that older low tech ships lacking floorfields and relying on fusion or fission for thrust are actually the hardest to detect.

Well, that is all for now. The next article will deal with the practical use of these sensors in Intercept. How to use them effectively and how to avoid being detected by them. Keep the solar wind to yer backside folks!

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.