I received this report from DeepSpaceTwo, now safely back at DSRS Copernicus. Since he can no longer explore deep space he has turned his attention to technology performance!
"It is common knowledge that the class of an engine does not determine a ship's acceleration, only its top speed. Afterburners increase both acceleration and top speed - hence their usefulness in combat. Military engines have a higher acceleration than civilian engines.
As a scientist I was intrigued with an assumption by an experienced pilot that if you set your ship into Inertial Flight Mode and use your afterburner you will accelerate to 9999 or until you run out of fuel. It got me thinking. I was fairly sure from experience that the rate of acceleration decreased as speed increased. I had assumed therefore that there would be a maximum speed that a ship could achieve and that it would not necessarily be the 9999 limit on a ships velocity indicator. Obviously you might run out of fuel before you hit top speed.
I decided to find out what was happening.
I chose measure the performance of several different classes of civilian and military ship, choosing a top and bottom class frame from each;
• A fully stripped out Talon with a 2800 capacity fuel tank
• A lightly equipped Ferret with its maximum 400 capacity fuel tank
• A Leviathan with a 2000 capacity fuel tank
• A Chimera with a 2000 capacity fuel tank
I'll give detailed data for the Leviathan - the other three ships behaved in the same way.
The Graph 1 shows how speed increases with burn time. The steepness of the curve is a measure of the rate of acceleration - the steeper the curve the faster you are acceleration. From a standing start, using afterburner in Inertial Flight Mode, the initial acceleration up to 5000 is very good, but acceleration starts to fall off after that; the conclusion is that there is little point trying to accelerate beyond 5000 using the afterburner. The change in speed is not straight line - it is a curve that gets flatter and flatter - a power law. It also gets close and closer to a final value - the maximum speed you can go. A graph that levels off slowly, approaching a final value is known as an asymptotic graph!
Although the fuel ran out before the top speed was reached I used the trend in change of acceleration to calculate (extrapolate) that the maximum speed achievable would be just under 7900.
The second graph shows the time it takes to increase your speed by 10 at different starting speeds. It shows that the time taken increases at an increasing rate; This is another way of showing that the changes are not straight line but are a power law. For example it takes 19 seconds to go from 7500 to 7510, but 91 seconds to go from 7800 to 7810 and a whopping 165 seconds to go from 7875 to 7885. Since fuel is burned at a constant rate this also means that every increase of 10 in speed takes more fuel as you go faster.
The third graph shows how speed is related to the amount of fuel used.
To accelerate from standing start to 6000 takes 50 units of fuel - equivalent to an average of speed increase of 120 per unit of fuel
50 units of fuel will also accelerate you from
• 6000 to 6700 (an average increase of 16 in speed per unit of fuel)
• 6700 to 6940 (an average increase of 5 in speed per unit of fuel)
• 7312 to 7377 (an average increase of 1 in speed per unit of fuel)
The trend continues until we can see that 100 units of fuel will accelerate you from 7874 to 7882 - equivalent to an 12.5 units of fuel for an increase in speed of 1!
All four ships have a maximum attainable speed of between 7800 and 7900
EDIT: What happens when I slow down?
Deceleration also uses your engines.
Graph 4 show a full acceleration / deceleration cycle in a Chimera:
It took 300 seconds to accelerate to 7120 and 415 seconds to slow down again, since the afterburner wasn't used in the slowing phase. The curves are symmetrical - the faster you are travelling the slower velocity changes occur under a constant thrust.
To slow down quickly and hence conserve fuel, just do a jump! (Thanks TJJ). If you are short of fuel this could be into a station if you can see it on the NavMap or know the coodinates or it could be just near to where you are.
Bingo fuel is equal to (class of Fulcrum Drive +10) - the extra 10 units of fuel allows for slowing down after the jump plus a bit to manoeuvre into the station you build or deploy!!
TJJ's comment about the effect of a star's gravity is a whole different ballgame. If you close the throttle, your speed indicator stays at zero, but you are drawn towards the star. I accelerated from 1425 to 2500 in around 90 seconds and then exploded. This was from an approach starting 25K from the star
If you cruise past a star at 2500 there is no measurable deviation on the direction of your flight - the effect is obviously subtle. Gravity slingshotting doesn't look like it's a goer unless Vice scales up the size of star's n the EM extension like he is scaling up the size of planets!
Mapping the gravity field around a star and measuring its effect on a ship will need a new set of experiments. Tempting!
[Edited on 30-1-2012 by DaveK]
:P
Visual aids. I love 'em. Especially graphs. 
