The Effect of Mass

As Dominium’s Flight Mechanics journey continues, I’m revelling in the nostalgia of all that school math/mechanics/physics from so long ago.

Now I have Newton’s Second Law(F=ma) in the code armoury, and all the various tunable ‘bits’ which affect movement and orientation (steering) I have set about establishing those basic configurations I mentioned previously, chiefly being;

  • Fighter
  • Hauler/Cruiser
  • Carrier
  • Capital Ship (an additional one)

Even with the in-engine Tweakers, determining nice configurations for each – even as a baseline – would be challenge enough. After all, I’m using ‘real world physics’, so I need ‘realistic’ values to plug into all the parameters. How heavy would a Capital ship actually be? How fast could it turn (or rather ‘how slow’!). No one knows, and simply ‘making stuff up’ would ultimately lead to a lot of ‘tuning’ effort. Effort I don’t have time for now. (Do not be alarmed however, proper tuning will be done by proper gameplay balancing later!)

Well, ‘extrapolation’ is the best bet I find. Also, comparitive ‘real world’ examples/references also help.

‘Real world’? You may ask… Yep, let’s do some research…

Fighter Configuration

We can presume fighters in Dominium (generally) will be in the same league as Jet Fighters here on good old Earth. A bit heavier and with spiffier engines/armour and so on. So, we pick a base line… one of my favourites (for looks anyway!) – the F15 Eagle

I then nab some basic stat’s from the F15 (with some liberties);

Size: 19.43 x 13.05 x 5.63
Mass : 12.79t
Thrust : 2 x 106.0 kN (max)

Size is in metres, mass in metric tonnes (1t = 1000kg), and the maximum potential thrust is in kilo-Newtons.

I then plugged these into the ‘Fighter’ configuration, and then tuned the non-physics aspects (such as Inertial Compensation, time to maximum thrust, etc.) Starting with the base line made it a lot easier to get something that felt suitable for a Fighter (nippy, responsive, agile, fun to fly).

Hauler / Cruiser Configuration

So, for the hauler/cruiser – we have a more appropriate reference! The Space Shuttle!

Size: 56.1 x 8.7 x 8.7 (no wingspan available)
Mass : 2030t
Thrust : 3 x 2,279 kN (max)

Sticking these numbers in, means at maximum thrust the (unladen) Space Shuttle can pull 0.343g – in a straight line. Not very exciting for a Space Game – but I wouldn’t complain if I were really on board!

Carrier Configuration

For a carrier, a ‘like for like’ reference, one of, if not the largest Aircraft Carriers in existence – the USS Nimitz

Size: 333.8 x 76.8 x 45(apprx)
Mass : 100,020t
Thrust : N / A

Hmm, so now we have a problem, no details on thrust – and even so it would probably be unsuitable for our purpose. But no worries, let’s presume we want a Carrier the same size and mass of the USS Nimitz – in space – to be able to accelerate at 0.1g…

F = Ma = 100020000(kg) x 0.1 x 9.81m/s^2(1g)
F = 98119620N or 98119.6kN

To match the meagre 0.343g linear acceleration of the Space Shuttle, our Carrier would need a staggering 336,865,359N
of thrust (or 148 RS-25 Space Shuttle Main Engines)!

I can also use the USS Nimitz stat’s to solve a more general issue.

Artists will model the ships, but with no real inclination of their physical mass, as a rule. Designers could knock all this out – but I have none to hand (other than me) and I haven’t got the time. But, this is something we can easily determine (fudge) with a spot of math…

To work out the approximate total mass of an object, you need it’s total volume, and the average density of the object (M = pV). We can take the values we need from the USS Nimitz – we have the mass already, and it’s rough volume. But, the USS Nimitz is not one huge cuboid, it’s all over the place. So, a rule of thumb, I simply halve the cuboid volume…

V = (333.8 x 76.8 x 45.4) / 2.0 = 576806.4m^3 (metres cubed)
M = 100020.0t

So the average density(p) is;

p = M/V = 100020.0 / 576806.4 = 0.1734 t/m^3

Although this is a (fairly gross) generalisation, it’s actually not that bad a basic figure to work with. The USS Nimitz is a fairly large object to take a sample average from; it has lots of bulkheads, open spaces, very heavily equipped spaces (like the reactor) and so on, pretty much like a spaceship would. Granted materials would be mostly different, as would the equipment involved, but these things balance out for my purposes and give me something to work with. The sheer size of the numbers involved reduce the impact of minor variations and discrepancies. Doing this with a car, for example, would yield a horrifically inaccurate result!

Now we have an ‘average density for any spaceship’, all I need to do is compute the volume of a model and use this formula to derive it’s ‘unladen mass’ for any of the ships. Huzzah!

Which brings us to… the unknown ‘Capital Ship’!

Capital Ship Configuration

No one has built one. Obviously. So we dive into the realms of pure speculation. Let’s say, a 2km long beast, on par with the shape of the USS Nimitz

Size : 2000.0 x 220 x 135
Mass : 5,149,980t (derived using average density)
Thrust:: 5,052,130 kN (0.1g)

I can assure you, you won’t want to ‘fly’ this 🙂 It turns like a dead stoat, and you have to post letters a week in advance to get it to stop.

Ain’t math wonderful?

Summary

So moving forward with this, every single ship will instantly provide ‘variation’ on the basic flight mechanic configuration assigned to it’s class, as each will have it’s own mass, and moment of inertia (the distance from the centre of mass to the furthest extent of the ship). I don’t have to edit/alter a single thing!

Every fighter will fly slightly differently, even though they have the same configuration. The system also takes ‘gross mass’ into account, so the more cargo you slap in your hauler, the more sluggish it will feel. You can combat this by installing/upgrading the Inertial Compensator, or the drive system, and so on. But care is needed, as the more equipment you add, the heavier you get 🙂

On top of this, we can adjust all the parameters for the control systems themselves, to increase the diversity and ‘feel’ across every ship.

I just can’t wait to play with this stuff for real 🙂

PS. Yes, I will try and get a video up and running – to at least show the four configurations in action. And yes, it’s something better ‘played’ than watched 😉 You never know, I may yet get a playable up and running…

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Author: Mak View all posts by

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