Realistic Accelleration...

[NuSoardGraphite]

In The Ultimate Vehicle it uses the model of 60" per turn as being 1G of accelleration. Those of us who are a little math-savvy know this to be wrong, wrong, wrong. Its a great, linear model for those looking for a number, but not a realistic one. In the text of TUV, it says that those looking for a more realistic model shouldn't have a problem coming up with one.

 

Lets do that now, shall we

 

Accelleration is generaly measured in G's, which is the number of "gravities" that is exerted upon the vehicle (and its occupants) during accelleration. 1 G is equal to about 9.8m/s/s, which we're going to round up to 10m/s/s for ease of math, and because that makes HERO movement of 5"/s/s equal to 1G of accelleration.

Now, The Ultimate Vehicle takes this number and multiplies it by 12 (12 segments/seconds in 1 turn) for its measurement of 60"/turn equals 1G of accelleration. However, this is not how accelleration works.

 

With constant accelleration, you add the rate of accelleration each second to the current speed to get the actual speed. For example, a Fighter craft that is accellerating at 1G (10m/s/s) will travel at 10m/s the first second, then add +10m for a speed of 20m/s, then add +10m for 30m/s (during the 3rd second of accelleration) so on and so forth.

 

So, going with that calculation, in HERO movement terms 1G of accelleration (5"/s/s) will allow a vehicle to travel a total of 390" in 1 turn.

 

With 5" of accelleration per segment, it looks like this:

 

Seg/Speed/Total" travelled

1 /5"/5"

2/10"/15"

3/15"/30"

4/20"/50"

5/25"/75"

6/30"/105"

7/35"/140"

8/40"/180"

9/45"/225"

10/50"/275"

11/55"/330"

12/60"/390"

 

As one can see, 390" (780 meters) is a fair distance travelled in a mere 12 seconds. 1G of accelleration is the realm of modern jet fightercraft, and even then only the worlds top craft exceed 1G, most averaging between .7 and .9 G's of accelleration.

 

Use a vehicles Combat Movement only to calculate accelleration. Do not use Non-combat movement, as this is merely an indication of the vehicles Top Speed...the maximum velocity to which it can accellerate, based on factors such as Drag/friction via atmospheric pressure, etc.

As per Hero5E pg 83, a vehicle may not accellerate in a phase more than its Combat Move.

 

Speaking of Top Speed, a vehicles Top Speed is the maximum speed it can accellerate to based on its streamlining against the friction and atmospheric pressure acting upon it to slow it down. This is represented via the Non-combat multiplier. Most ground vehicles (depending on mode of transport and design) have a non-combat multiplier between x2 and x4 (though very streamlined vehicles such as rocket cars built for speed can have a x8) Aerial vehicles can have between X4 and x8 with supersonic aircraft, such as most military jet fighters having around X16 (or possibly higher). Only superfast futuristic vehicles should have X32 or higher.

Now for something a little different. Instead of sticking to the simple model of +5pts for X2 non-combat movement, use a range of non-combat movement instead of the usual x2, x4, x8 etc. With this method the point cost breaks down thusly;

 

+5pts x2

+10pts x3-x4

+15pts x5-x8

+20pts x9-x16

+25pts x17-x32

etc.

 

Using this method, you can get accurate accelleration models, then use the most appropriate modifier to get closest to the vehicles actual Top Speed to be as accurate as possible.

 

As an example, lets use the F/A-22 Raptor. The Raptor's combat weight is around 60,000lbs. It has a motive thrust of 70,000lbs and thus has a thrust to mas ratio of 1.16, from which we derive its G-accelleration. An accelleration factor of 1.16 is equal to 452.4" travelled in 1 turn of accelleration. We'll round that down to 450" for ease of math. Since the Raptor is a highly responsive fighter craft, we've decided to give it a Speed 5. At speed 5, 30" of Combat Move equals exactly 450" travelled in 1 turn. Thus, the Raptor has a Combat Move of 30" per phase. (doesn't seem like much, does it?)

The Raptors Top Speed is rated at Mach 1.58 (actually, this isn't listed as "Top Speed" but as "Supercruise") which is 1706.4kph. At 30" per phase of accelleration, the Raptor needs a non-combat multiplier of x19 to achieve at least that much (x19 gets it to 1710..ony 4.4kph off!)

There you have it! The Raptor accellerates at 1.16G, which is 30"/phase at Speed 5, and can reach speeds of 2850" per turn or mach 1.58!

Of course, the Raptor can also use Afterburner and when it does this its accelleration increases as well as its top speed. Its speed when using Reheat is listed at Mach 1.7 or 1836kph. For this, we have to add to Combat Movement, since basic accelleration will be increased as well. Adding +3" to the Raptor's Combat Move (to 33") will increase its accelleration to 1.26G's (495") which increases its Top Speed to 1881kph (Mach 1.74)

 

Using this method, you can easily model Fightercraft from real-world and fictional sources (such as many mecha writeups).

 

A word on writing up ground vehicles and water vehicles: the above was primarily aimed at aerial vehicles. Ground and water vehicles conform to a whole host of different calculations for getting their accelleration from the power of their engines. In general, ground vehicles have a Power to Mass ratio thats similar to a flying vehicles thrust to mass ratio (which generates their G's of accelleration) but with Ground vehicles, the Power to Mass ratio works somewhat differently since its Torque doing the work and not actual raw thrust as in a Jet fighter. But hey, you don't have to get THAT realistic, do you? Just use a vehicles Power to Mass ratio to get its accelleration (like with the listed statistics of modern tanks) and keep the non-combat multiplier to a reasonable X4 or so and you should be okay.

 

A note on VTOL vehicles. If the vehicle doesn't have a lifting body shape or wings to give it lift (for example, most mecha do not have a lifting body shape or wings), the vehicle must use a portion of its thrust for lift. This means that the vehicle cannot use its full motive thrust to calculate its Accelleration with. Example:

 

The Guardian is a high mobility mecha that weighs 18 tons. It has 40,000lbs of thrust, which would give it an accelleration rating of 1.1G's of thrust....in space. On a planet with Earth normal gravity, it must use 36,000lbs of its thrust to cancel its weight in order for it to fly, leaving a mere 4000lbs of thrust left for accelleration. Thus while planetside, it has a G accelleration rating of .1G's or a mere combat move of 4" per phase. Thats way too slow to bother with, thus the Guardian is best served by using its thrusters to assist in jumps while planetside.

It is for this reason that mecha such as the Mobile Suits of Gundam and VF's of Macross (in Battloid mode, in any case) do not use their thrusters for full flight while in an atmosphere. Though they could use them to "hover" and maneuver somewhat while mid-air (they do this a lot in Macross), using them for long-range transportation is generally a waste of fuel. Remember though, as long as a vehicle has more motive thrust than it has loaded mass, it can remain airborne, irregardless of how slow it might actually be to accellerate.

 

So, what do ya think? Anything I missed, or was incorrect on. (I'm sure I missed something in there...)

[Intrope]

Re: Realistic Accelleration...

 

This looks good to me! BTW, you have your Non-combat multiple costs off (you started at x2 = 5pts, that should be x4).

 

FYI, if you are using in-between multiple values (like the x19 for the Raptor) you can compute a partial point value:

 

5 * [ (ln multiple)/(ln 2) ] - 5

 

(ln == natural log here)

for the Raptor's x19, that's 16 pts.

[DrFurious]

Re: Realistic Accelleration...

 

So, going with that calculation, in HERO movement terms 1G of accelleration (5"/s/s) will allow a vehicle to travel a total of 390" in 1 turn.

 

With 5" of accelleration per segment, it looks like this:

 

Seg/Speed/Total" travelled

1 /5"/5"

2/10"/15"

3/15"/30"

4/20"/50"

5/25"/75"

6/30"/105"

7/35"/140"

8/40"/180"

9/45"/225"

10/50"/275"

11/55"/330"

12/60"/390"

 

Well if you are going with a more "realistic model" then your calculated distances are off. Some formulas:

 

d(t) = d0 + v0 * t + 0.5 * a * t^2

v(t) = v0 + a * t

 

a : acceleration is 1 G (a constant)

d0 : initial distance (assume it is zero here)

v0 : initial velocity (assume it is zero here)

 

so we get the following:

 

d(t) = 0.5 * G * t^2

v(t) = G * t (as you have above)

 

 

d(1) = 0.5 * 5" * 1*1 = 2.5 "

d(2) = 0.5 * 5" * 2*2 = 10 "

d(3) = 0.5 * 5" * 3*3 = 22.5"

etc..

 

So you're a bit off but the curves remain close. At this point, I'm losing interest so I'll let someone else take over.

[NuSoardGraphite]

Re: Realistic Accelleration...

 

This looks good to me! BTW' date=' you have your Non-combat multiple costs off (you started at x2 = 5pts, that should be x4).[/quote']

 

yer right. I flaked on that (had kids crawling on me at the time) and the initial should be X2 at +0 cost. Each additional after that should be 5pts less...

 

FYI, if you are using in-between multiple values (like the x19 for the Raptor) you can compute a partial point value:

 

5 * [ (ln multiple)/(ln 2) ] - 5

 

(ln == natural log here)

for the Raptor's x19, that's 16 pts.

 

Thats certainly possible. Thanks for mentioning it. Some Gm's would probably find this more appropriate.

[NuSoardGraphite]

Re: Realistic Accelleration...

 

Well if you are going with a more "realistic model" then your calculated distances are off. Some formulas:

 

d(t) = d0 + v0 * t + 0.5 * a * t^2

v(t) = v0 + a * t

 

a : acceleration is 1 G (a constant)

d0 : initial distance (assume it is zero here)

v0 : initial velocity (assume it is zero here)

 

so we get the following:

 

d(t) = 0.5 * G * t^2

v(t) = G * t (as you have above)

 

 

d(1) = 0.5 * 5" * 1*1 = 2.5 "

d(2) = 0.5 * 5" * 2*2 = 10 "

d(3) = 0.5 * 5" * 3*3 = 22.5"

etc..

 

 

Hmmm...okay. So why is there a "0.5" in the distance calculation (I am very much math impaired you see)?