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Old 04-01-2017, 02:43 PM   #1
hal
 
Join Date: Aug 2004
Location: Buffalo, New York
Default GURPS ULTRATECH ballistics?

Hello Folks,
I've been promising myself that someday, I'd examine the rules for liquid propellants for use in Ultratech weapons of the future. Today, seems to be that day.

First, the background:
Douglas Cole produced a spreadsheet that gave a formula for approximating cartridge damage from real world data. From that original spreadsheet, I revised it for my own needs so I could simply enter in the bullet weight by grains, velocity by feet per second, diameter in inches, and it would give me a GURPS 4e bullet damage value. It was so good, that when I creaed a database for black powder weapons of various bullets in grain weight, plus velocity of bullet achieved as muzzle velocity - I was able to compute the GURPS damages that largely matched what was in the GURPS ADVENTURE GUNS supplement.

So, let's take a historical cartridge listed in my database. It is the .25-25 Stevens center fire cartridge produced in 1895 with a 66 grain bullet and a muzzle velocity of 1180 feet per second. The estimated muzzle energy seems to have been 204 foot pounds per the calculations.

In GURPS terms, such a weapon would have a 2d6 damage rating.

So, how do back track the stats for a bullet as if this weapon were using liquid propellants (in order to determine what the weapon's muzzle velocity has to be to achieve the damage listed in the rules as listed below:

"Boosted velocity dumps extra propellant into the firing chamber: increase the piercing damage by +1 per die and multiply range by 1.3. Each counts as 1.5 shots for purposes of draining the propellant bottle."

So, a weapon that normally does 2d6 damage, with a 66 grain bullet, has to have a velocity of 1180 feet per second - regardless of whether it was produced by black powder, modern gun powder, or even liquid propellant. In order to achieve an average damage of 9 points instead of 7, we'd need to increase the velocity if we keep the grain weight the same.

So how much of a velocity increase are we talking about?

We'd need to get the velocity from 1180 up to 1490 feet per second. Those of you who have a better grasp of the "joules per" weight measure or joules per volume measure of the propellant can chime in, or you can perhaps say "Hey Hal, nice idea in theory, but... that doesn't match my calculations."


So, showing all work:

ft/lbs (cell A57) =H57*I57^2/450395

Data in cells H57 was weight of bullet in Grains, and I57 was Velocity in feet per second (in this case, 66 grains and 1180 feet per second)

ME in J. (cell B57) =1.35581794833189*A57 (or Ft/lbs value)

dam pts (cell C57) =ROUND(SQRT((B57^1.04)/((PI()*((E57/39.37)/2)^2)^0.314))/13.3926,1)

E57 is bullet diameter in inches, B57 is Muzzle energy in joules.

Damage Dice (Cell D57) =CONCATENATE(INT(C57/3.5),"d+",FLOOR(3.5*(C57/3.5-INT(C57/3.5)),1))

C57 = average bullet damage

Bullet Diameter in inches (Cell E57) =0.25
Bullet weight in Grains (Cell H57) =66
Bullet Velocity in feet per second (Cell I57)=1180


Those were all based on the spreadsheet that Douglas Cole built. Hope this helps people to visualize their stats for how the weapons function.

Using a modern day bullet such as the .44 colt with its 210 grain bullet, 660 feet per second velocity, and its listed muzzle energy of 206, when I plunk those values into the spreadsheet, I get 1d6+2 damage (modern pistol round). The 45 ACP on the other hand, when entered into the spreadsheet, shows that for a round listed as being a jacketed hallow point at 185 grains, 1000 feet per second muzzle velocity - that would be, per the spreadsheet, roughly 2d+1.

Now the fun part would be - to try and figure out what the bullet weights of the Caseless Ammo in GURPS ULTRATECH are by weight, and figure out what the muzzle velocity has to be based on the damage ratings given in GURPS ULTRATECH.

The 7.5mm caseless ammunition is roughly a .30 caliber gun. Using the 7.5mm Swiss Army Revolver Stats for the bullet (from CARTRIDGES OF THE WORLD), that's a 110 grain bullet. The muzzle velocity of the gun, in order to achieve a 2d6+2 damage rating, would require a velocity of 1380 feet per second.

In theory, it should be possible - using the stats above, to come up with a formla that gives us the following:

Bullet weight in ULTRATECH - which is supposed to be the combined weight of the bullet plus its propellant and packaging..
Caseless ammo is what - a ratio of bullet weight to propellant? If for instance, the weight of a round is 1/3rd bullet weight, and 2/3rds propellant - we should be able to get the joules per mass of a given propellant in order to be able to custom build bullets for use with GURPS ULTRATECH. Using real world bullet weights of modern bullets, and then using the Joules per Gram measurement or Joules per grain (I know I'm mixing Imperial with Metric darn it!) - we should be able to specify the stats for a 7.6mm round, a 5.56mm round, or a 11.5mm round easily enough.

Just thinking...
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Old 04-01-2017, 03:21 PM   #2
Fred Brackin
 
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Default Re: GURPS ULTRATECH ballistics?

Quote:
Originally Posted by hal View Post
So, a weapon that normally does 2d6 damage, with a 66 grain bullet, has to have a velocity of 1180 feet per second - regardless of whether it was produced by black powder, modern gun powder, or even liquid propellant. In order to achieve an average damage of 9 points instead of 7, we'd need to increase the velocity if we keep the grain weight the same.

So how much of a velocity increase are we talking about?

We'd need to get the velocity from 1180 up to 1490 feet per second. ..
Hm, what I'd do is divide 1180 by 7 getting 168 and some decimals. Then I'd multiply that by 2 and add it to the 1180 getting 1517 (and some more decimals). Or even more simply I'd multiply 1180 by 1.2857 and get 1517.

The situation you've outlined is one where damage increased is linear with velocity increase.
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Old 04-01-2017, 03:39 PM   #3
hal
 
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Default Re: GURPS ULTRATECH ballistics?

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Originally Posted by Fred Brackin View Post
Hm, what I'd do is divide 1180 by 7 getting 168 and some decimals. Then I'd multiply that by 2 and add it to the 1180 getting 1517 (and some more decimals). Or even more simply I'd multiply 1180 by 1.2857 and get 1517.

The situation you've outlined is one where damage increased is linear with velocity increase.
Unfortunately from my perspective, that seems to line up with what they're using with GURPS ADVENTURE GUNS. The stats I got matched up almost exactly (as far as damage goes).

What I probably should do is grab some stats on modern weapons and compare them against GURPS HIGH TECH just to see if they vary or not. If so, perhaps use the methodology you suggest above just to see how it works. In fact, when I get the chance (got errands to do just now), I'll try it your way and see how it works with the original Black Powder database to see where they vary or not.

The goal I think, is to get an "average damage value" which does factor in velocity squared. The divisor of 450395 is likely a conversion factor between imperial units and metrics. I'm going to have to find the original spreadsheet Doug gave me to confirm.

What I didn't understand in Doug's sheet were the metrics of 1/2 damage, etc and expansion of gases etc.

Hopefully, Doug himself will chime in on this, because I dimly recall I confirmed my formula with him before going with it...

Catch you in about 60 to 90 minutes
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Old 04-01-2017, 05:55 PM   #4
DouglasCole
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Default Re: GURPS ULTRATECH ballistics?

I'll get back to this in an hour or so; dinnertime now.
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Old 04-01-2017, 06:49 PM   #5
hal
 
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Default Re: GURPS ULTRATECH ballistics?

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Originally Posted by DouglasCole View Post
I'll get back to this in an hour or so; dinnertime now.
Thanks Doug.

I'm looking at your formulas for the EASY CONVERSIONS tab, and for the most part, I suspect that this is what I was originally looking at when I first made my spreadsheet.

Now, I'm looking at another formula that lists the formula of Muzzle energy as being equal to:

Muzzle Energy in J = Projectile Mass(g) x (velocity in m/sec)^2/2011

I was trying to figure out why the 2011 constant for the divisor was there, until I spotted the formula where Velocity in meters per second was spelled out. This formula works out to:

Velocity in m/sec = (Muzzle Energy(J)/Projectile Mass(in grams))^.5 x 44.84

When I factored out the various things, I came to realize the 2011 value is actually the 44.84 value squared (but rounded off). Even so, the two formulas that I'm looking at for Muzzle Energy in Joules (yours and Greg's) are off by about .528 percent (ie, negligible really).

More in my next post...
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Old 04-01-2017, 07:30 PM   #6
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Default Re: GURPS ULTRATECH ballistics?

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Originally Posted by hal View Post
The goal I think, is to get an "average damage value" which does factor in velocity squared. The divisor of 450395 is likely a conversion factor between imperial units and metrics. I'm going to have to find the original spreadsheet Doug gave me to confirm.
Likely. There are a lot of funky units at play here. Grains, grams, pounds . . .

Quote:
What I didn't understand in Doug's sheet were the metrics of 1/2 damage, etc and expansion of gases etc.

Hopefully, Doug himself will chime in on this, because I dimly recall I confirmed my formula with him before going with it...

Catch you in about 60 to 90 minutes
The 1/2D calculations used an exponential fall off of velocity based on sectional density. It's close enough to give a good approximation in the supersonic regime but isn't nearly as good as a real ballistics table.

the gas expansion stuff is just a representation of how much energy goes into the bullet, based on integrating force over distance. I used the ideal gas law to figure out how the pressure falls off as the volume expands (the volume is the chamber plus the barrel) and then just integrated Force = Pressure x bullet area over the barrel length.

Expansion is something I just plug into my penetration and wound channel equation - increase bullet caliber by the expansion ratio, and let the rest take care of itself.

For basic bullets thrown from ultra-tech guns, you're doing the right idea - take best guesses for caliber, mass, and velocity, and adjust mass and velocity so they're not crazy-town and the damage is about right. The assumptions going into UT were not all rational and logical and if A then B, so it might not work every time.
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Old 04-01-2017, 07:36 PM   #7
hal
 
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Default Re: GURPS ULTRATECH ballistics?

Ok, so I decided to try an analyze the different approaches to damage values, muzzle velocity, Joules per gram of a given substance etc - all the while using both GUNS, GUNS, GUNS by Greg Porter and the spreadsheet that you devised, along with the formulas for what I used in order to that I could use specific real world data of bullet weight in Grains and bullet velocity in feet per second (how the data is displayed in CARTRIDGES OF THE WORLD 8th edition - I know it is at a higher edition than 8th as of today!).

So, here's what I did. I used both of Greg's formulas - Muzzle Velocity and Muzzle Energy, to double check against each other, and the original real values for any given bullet (the one I listed earlier with a bullet mass of 130 grains and a bullet velocity of 1180 feet per second).

Using your formula given on your spreadsheet, the Muzzle Energy for a 130 grain bullet travelling 1180 feet per second works out to 544.8475086 Joules. Greg Porter's formula gives a value of 541.9681402 Joules.

Using only Greg's formula for Muzzle Velocity (I didn't try to reverse engineer your formula, but I'd imagine if I did reverse engineer your formula, it would be slightly different than Greg's formula)...

(544.8475086/8.4238583)^.5 x 44.84 = 360.6181343 Meters per second or 1183.1304 Feet per second.

Using Greg's calculation formula for Joules in the equation:

(541.9681402/8.4238583)^.5 x 44.84 = 1180

So, it isn't surprising that using only Greg's formulas for Muzzle Velocity and Muzzle Energy will be internally self-consistent in order to double check things.

Your formula for Joules is:

.5 * Weight in grams/1000 * (Velocity in meters/sec divided by 1000)^2

I'm guessing that you were trying to use the formula such that it used unit measures of Kg and Kilometers

That's my guess overall.
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Old 04-01-2017, 07:41 PM   #8
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Default Re: GURPS ULTRATECH ballistics?

Quote:
Originally Posted by hal View Post

Your formula for Joules is:

.5 * Weight in grams/1000 * (Velocity in meters/sec divided by 1000)^2

I'm guessing that you were trying to use the formula such that it used unit measures of Kg and Kilometers

That's my guess overall.
You sure that second m/s is divided by 1000? A Joule is a kg m/s^2, which is mass in kg, velocity in m/s. There shouldn't be a second divisor there.
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Old 04-01-2017, 08:07 PM   #9
hal
 
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Default Re: GURPS ULTRATECH ballistics?

Quote:
Originally Posted by DouglasCole View Post
Likely. There are a lot of funky units at play here. Grains, grams, pounds . . .



The 1/2D calculations used an exponential fall off of velocity based on sectional density. It's close enough to give a good approximation in the supersonic regime but isn't nearly as good as a real ballistics table.

the gas expansion stuff is just a representation of how much energy goes into the bullet, based on integrating force over distance. I used the ideal gas law to figure out how the pressure falls off as the volume expands (the volume is the chamber plus the barrel) and then just integrated Force = Pressure x bullet area over the barrel length.

Expansion is something I just plug into my penetration and wound channel equation - increase bullet caliber by the expansion ratio, and let the rest take care of itself.

For basic bullets thrown from ultra-tech guns, you're doing the right idea - take best guesses for caliber, mass, and velocity, and adjust mass and velocity so they're not crazy-town and the damage is about right. The assumptions going into UT were not all rational and logical and if A then B, so it might not work every time.
Thanks for the comments Doug. I kind of knew that any time you have a final damage value that is based on Mass times velocity Squared, I knew that this would be a function value where you fill in 1 value, the remainder would automatically spit out.

My next post is going to be based on some conjecture, and I will use the historical data for a 7.5mm round gun from the past designed in 1883, using black powder (presumably) that was used until 1903 in the Swiss army. Presumably, that round had satisfactory characteristics for flight, that it was worth retaining. Its mass was 110 grains (range given is 102 to 110, so let's use the upper for this example).
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Old 04-01-2017, 08:21 PM   #10
hal
 
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Default Re: GURPS ULTRATECH ballistics?

Quote:
Originally Posted by DouglasCole View Post
You sure that second m/s is divided by 1000? A Joule is a kg m/s^2, which is mass in kg, velocity in m/s. There shouldn't be a second divisor there.
Double checking...

130 grain bullet is 8.4238583 grams
.38 inch Diameter is 9.652mm
1180 feet per second is 359.6639885 meters per second

Plugging the same data into your spreadsheet, and then looking at your "used column" (Column F in the Excel spreadsheet titled as Ballistics Model Jan1 - 2012)

Grains 130 - used .008424 kg
Inches .38 - used .009652 m
FPS 1180 - used 359.664 m/s

Your formula for Joules lists the formula =0.5*D3*D6^2 where D3 is Kg, D6 is M/s

Sorry - was correct on one, incorrect on the other...

Only the one is divided by 1,000 to get it into units of Kilograms. The meter's per second is not km per second... (bad Hal, no cookies for you!)
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