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What's your Holy Grail of Spudguns?

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Unread postAuthor: Ragnarok » Mon Jan 14, 2008 6:40 am

rna_duelers wrote:I'm 100% on the side that says it won't make .5km at 3 degrees elevation.

Looks like I need 30 bar, a dart and a 500 metre firing range then - wherever the hell you get one of those these days.

Well, when I've got those things, I shall try, and we shall see.
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Unread postAuthor: MrCrowley » Mon Jan 14, 2008 7:11 am

Ragnarok wrote:To go 500 metres in 2.5 seconds, I'd need an average speed of 200 metres a second. If I'm launching a low drag dart at 240, I don't think that 200 m/s average is hopelessly optimistic.


Yeah I figured that much out :)

An average speed of 200m/s is quite high, maybe for the first 250m I could see speeds about 200-250m/s, but after that the speed will dramitcally decrease, drag will dramitcally increase, and dart will start to drop.

Just look at figures from bow and arrows like me and JSR said before, an arrow is essentially a long dart, and they have huge curves in their projectile parabola.

I'm sure you can reach the 500m, but at only 3" degree elevation, not likely.
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Unread postAuthor: Ragnarok » Mon Jan 14, 2008 8:14 am

MrCrowley wrote:An average speed of 200m/s is quite high, maybe for the first 250m I could see speeds about 200-250m/s, but after that the speed will dramitcally decrease, drag will dramitcally increase, and dart will start to drop.

How do you figure drag increases? Drag will decrease with the velocity. Drag will be highest at the start, and using that information...

Assuming a reasonable drag coefficent of 0.1, about what you would expect from a good dart, and checking my dart design, it has a weight of 16 grams, and a cross sectional area of about .56 cm<sup>2</sup>.
240 m/s at the muzzle, and that's if I use a 1.2m barrel - if I increase that, I can obviously get more.

Feeding that into the drag equation, the drag force at the start is about ~0.2N, and that is it's highest value. ~0.2N on a 16g dart will slow it by 12.2 m/s per second of flight.
As speed decreases, the acceleration will also decrease, but to keep it simple, I'll use the peak value, which will actually over compensate for drag.
Solving that, you find the dart (launched at 240 m/s) will travel 500 metres in 2.2 seconds - it's still doing over 200 m/s on impact. That time doesn't include the slightly longer arc of the parabola than the direct point to point, but we know the drag is a bit high, so it sort of matches out.
And 2.2 seconds is 23.7 metres of drop. Tan (3) * 500 is 26.2 metres of rise, so 3 degrees will actually over shoot 500 metres.

Ok, lets say I've completely messed up the drag coefficient. If I double the drag coefficient to 0.2, which would be pretty poor for a dart really - it rises to 2.37 seconds travel (190 m/s impact) - 27.45 metres of drop, which can be compensated for by increasing the angle to 3.2 degrees.

Before I had done the maths, I would have completely agreed with you guys, I admit, it sounds almost impossible, but having done the sums, I have to say otherwise.
I hadn't realised how much difference a low cross sectional area and a low drag co-efficient will make to how far a 800 fps dart can go.

More muzzle velocity can drop that angle even more. 30 bar helium and a 2 metre barrel would allow the dart to go that far on just 1.5 degrees elevation, but the muzzle velocity would be almost Mach 1 there.
Mind you with that velocity, I could fire the dart over 3 kilometres with a large enough elevation. Tempting though that is, it would be impossible to see, and would come down with as much energy as a .22 rifle - also it would be a lot pointier...
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Unread postAuthor: jackssmirkingrevenge » Mon Jan 14, 2008 8:17 am

What do you calculate the maximum range (at the theoretical optimal 45 degree angle) would be then?

edit: I looked up some firearm data, the following is Weapon or cartridge - Effective Range (yards) and Maximum Range (yards)

Sling 20 100
Short Bow 100 200
Crossbow 200 350
Long Bow 250 400
Hand Cannon 10 250
Turkish Bow 300 800
Matchlock 25 350
Harquebus 40 500
Flintlock Musket 60 800
Flintlock Rifle 100 1000
Percussion Musket 75 1000
Prussian Needle Gun 300 2000
Springfield .45-70 Rifle 500 2800
Krag .30-40 Rifle 500 3300
M1903 Springfield .30 cal 600 3500
M1 Garand .30 cal 600 3500
M14 7.62 mm 500 4300
M16 5.56 mm 500 3600
M1911 .45 ACP 50 1900
M9 9 mm 50 1800
.38Spl Revolver 50 1700
.357 Magnum Revolver 100 2400
AK47 7.62x39 mm 350 3500
AK74 5.4x39 mm 350 3700
M40A3 .308 rifle 1200 4300
M82 .50 Cal Rifle 2500 7500

source

I still think your data is optimistic.
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Unread postAuthor: Hotwired » Mon Jan 14, 2008 9:10 am

Maximum range @ 45 according to GGDT should be not too far from 630m with a projectile around 80g

I wouldn't be comfortable using the QEV piloting system at 450psi.


500m is possible at 3 degrees though given enough height...
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Unread postAuthor: Ragnarok » Mon Jan 14, 2008 9:25 am

jackssmirkingrevenge wrote:What do you calculate the maximum range (at the theoretical optimal 45 degree angle) would be then?

Well, of course, that 45<sup>o</sup> angle only applies when there is no drag. When there is, you need to drop it a certain amount.

With 435 psi regular air, a 120cm barrel and the 0.1 drag coefficent, the max range with said dart would be just under 3.2 km, 40 degree angle, 26 seconds in the air, 840m apogee.
With the helium extreme, max range would be just over 4.5 km, 39 degrees, 32 seconds, and an apogee of 1270m. Energy on return to the ground would be about 150 ft-lbs.
The 0.2 coefficent which I used for the other long range calculation cuts a far amount off the range, about a third in both cases.

If you still don't want to believe my maths, fair enough. I've tried to set out a set of calculations that are designed to show the numbers are in the right sort of range, and you can confirm the values quite easily. Sure, they cut a couple of corners, but nothing that condemns them as wildly inaccurate.

When you bring up firearms effective ranges, that's quite a different thing. That has to include accuracy, terminal ballistics, and other things. But let's take the NATO 7.62mm and 5.56 figures there for the sake of argument. Those are both supposed to have a 500 yard effective range, a bit less than 500 metres, but close enough.

To hit a target at 500 metres, the 5.56 will need to increase it it's firing angle to only 0.2 degrees to compensate for the drop, the 7.62 would need 0.3 degrees - and I wasn't even that sure of the drag coefficient so I deliberately guessed it quite high!
Why should what is a pretty high velocity cannon with a projectile optimised for low drag, rather than killing potential, not have the potential to fire the same distance with 3 degrees? - not a few tenths like with regular rifles, but whole degrees.

Also, you've got the M1911 on that list, which is convenient, because that has around the same sort of muzzle velocity and energy as HEAL would. The round has a much larger area and is much less optimised for range, so it will decelerate faster, but that still has a maximum range of well over a mile, so it's logical HEAL could at least equal that.

It might not hit accurately at anything like that distance, but I think the distance itself is achievable.

@Hotwired: If I were doing it, I would have an optimised dart, and GGDT's calculator is useless for working out those things. The piloting will need some changes before I can manage that of course, but that's not too hard.

Anyway, I've laid down all the facts I think I need to for now, if it hasn't been settled yet, it's not going to be soon, and in the meantime we're flooding this thread.
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Unread postAuthor: jackssmirkingrevenge » Mon Jan 14, 2008 9:36 am

you've got the M1911 on that list, which is convenient, because that has around the same sort of muzzle velocity and energy as HEAL would. The round has a much larger area and is much less optimised for range, so it will decelerate faster, but that still has a maximum range of well over a mile, so it's logical HEAL could at least equal that.


Not disputing that at all, especially with a streamlined dart as opposed to the lumpy 45 slug, it's the 3º angle that I have a problem with.
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Unread postAuthor: Ragnarok » Mon Jan 14, 2008 10:46 am

jackssmirkingrevenge wrote:Not disputing that at all, especially with a streamlined dart as opposed to the lumpy 45 slug, it's the 3º angle that I have a problem with.

Well, you've read what I had to say about the maths of a 3 degree angle equating to about 500 metres. That method to an approximation was simplified, but it doesn't cut too many corners - could you tell me where you think I went wrong with the calculations? Drag, bullet drop, or the rise from the increased angle?

Because I'm a bit bored, I'll go over it again, without omitting the information I did before.

Drag force is -<sup>1</sup>/<sub>2</sub>*drag coefficient*air density*area*velocity<sup>2</sup>

The minus sign means it's against the direction of movement. I ommitted it earlier for writing the forces, but I did keep it in the equations. If I put the various numbers into that:
Air Density: 1.2 kgm<sup>3</sup>
Drag Coefficient: 0.1 (but, if you prefer, 0.2)
Area: 0.56 cm<sup>2</sup>
Velocity: 240 m/s

You need to remember to put the area in square metres, but it's in square centimetres for the moment because it looks nicer. Output from the equation is in Newtons
All those numbers condense to -0.2 N or -0.4N depending on your drag co-efficient (or C<sub>D</sub>). I will use -0.2N in the calculations, but you can return and use -0.4 if you want.

To get the accleration, we divide by the mass, because:
F = m*a
and therefore: a = <sup>F</sup>/<sub>m</sub>
M needs to be in kilos, which is 0.016kg for this dart design.
So, a is -12 m/s<sup>2</sup>

Now we know that, we need to find time in the air so drop due to gravity can be found. For that, we need:
s = u*t + <sup>1</sup>/<sub>2</sub>a*t<sup>2</sup>

Or, with the values: 500 = 240*t + <sup>1</sup>/<sub>2</sub>-12*t<sup>2</sup>
As I said before, I am assuming drag is always it's maximum value to simplify it a bit.
We need that in terms of t (time) so we simplify to:
- 3*t<sup>2</sup> + 120*t - 250 = 0

Which is of the form ax<sup>2</sup> + bx + c = 0
So using the quadratic formula to find the values that solve that: Image
I find that the solutions are: 2.20487, and 37.79513
The 37.79513 is a result of the fact I assumed the drag force was constant. If it were, the round would slow, then could actually turn round and hit the target again. Because of that assumption, it's ignored now.

To find the drop, I'll need s = u*t + <sup>1</sup>/<sub>2</sub>a*t<sup>2</sup> again.
In this case, u is zero, the round is not initially falling. a is 9.81m/s<sup>2</sup>, acceleration in free fall.
S is therefore 23.845m. This is the drop of the round. The launch angle will therefore need to be sufficient to counter this drop.

Dividing 23.845 by 500, I get 0.04769. The tan<sup>-1</sup> of this number will give our angle.
Tan<sup>-1</sup> (0.04769) is 2.73<sup>o</sup>.

The number at the end is actually under the 3 degrees I was stating. Unless you can find a flaw in my logic or maths, I have to say, I think it's right.

EDIT: Damned hotlink blocking images. Hopefully it will work this time.
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Unread postAuthor: ALIHISGREAT » Mon Jan 14, 2008 12:20 pm

@ALI: Not hugely far I would say, paintballs have low sectional density, and slow down pretty fast.


yeah i suppose, although i'm thinking of getting some 17.27mm (11/16") steel bbs which should be good although they will have a crap drag coefficient :(

and as for the maths i don't doubt it.. mainly because i got bored arter the first line :D

and i'm with hotwired, a qev at 450psi could be dangerous if i ever take my planned piston gun up to that kind of pressure i will make a 22mm piston as the pilot, although it depends how you get on with your qev at 400psi and the piston pilot will mean i can go even higher (if my pump and arms allow me) as JFC has a pressure rating of 500psi but has been tested to 1000 without failing.
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Unread postAuthor: Ragnarok » Mon Jan 14, 2008 12:57 pm

ALIHISGREAT wrote:yeah i suppose, although i'm thinking of getting some 17.27mm (11/16") steel bbs which should be good although they will have a crap drag coefficient

Well, I ran the 1000 fps paintballs through the calculator, and it says about 200 yards maximum, which is quite a bit for paintballs, but my experience tells me that you can't expect to see them in the air except very rarely.
The steel BBs... well, if I have a velocity, I can predict your range.
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Unread postAuthor: ALIHISGREAT » Mon Jan 14, 2008 1:11 pm

Ragnarok wrote:
ALIHISGREAT wrote:yeah i suppose, although i'm thinking of getting some 17.27mm (11/16") steel bbs which should be good although they will have a crap drag coefficient

Well, I ran the 1000 fps paintballs through the calculator, and it says about 200 yards maximum, which is quite a bit for paintballs, but my experience tells me that you can't expect to see them in the air except very rarely.
The steel BBs... well, if I have a velocity, I can predict your range.


ok well first i will work out the wieght which should be ~12g and Poland_spud kindly put some stats through ggdt for my 400psi piston gun and for a 15g projectile he got 209.8m/s (685m/s) for a 15g projectile so i reckon a 12g projectile at 450psi would get ~800m/s?

feel free to prove me wrong, the specs are on this page http://www.spudfiles.com/forums/400psi-piston-vavle-t12445,start,60.html but obviously the operating pressure would be 450psi :)
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Unread postAuthor: Ragnarok » Mon Jan 14, 2008 1:57 pm

I personally would have come up with a weight of 20.7g for a 11/16" steel ball bearing. So, getting out GGDT, that's 198 m/s (408J) ...

That should be a very respectable 700 yards maximum, which sounds about right to me for a sphere of that size at that speed, I put them 450 with Behemoth, which was only about half that power. You'll obviously need to exercise caution with that sort of range.
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Unread postAuthor: ALIHISGREAT » Mon Jan 14, 2008 2:32 pm

You'll obviously need to exercise caution with that sort of range.


i have some fields i can shoot over with 2700yards of just fields :D

and i must have got it wrong somewhere, i will try again.

hmm 408j whats that in imperial? ooh as good as 300ft/lbs i better get a good backstop sorted out :twisted:
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Unread postAuthor: Hotwired » Mon Jan 14, 2008 6:02 pm

I'm a big fan of practical results so most theories going past me get a pinch of salt.

A 16g dart from a 1200mm x 20mm barrel @ 3 degrees with a chamber of say 1000mm x 20mm of 450psi air behind it to go 500m...

...is certainly pushing the boundaries of what I consider likely.


As a practical and negatively optimistic type, what I'd expect when in field conditions is for a high speed dart at that angle to zip into the ground significantly short of 500m and require a metal detector to find it again.

I'm open to being proved wrong by the ultimate test of a physical demonstration though.
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Unread postAuthor: ALIHISGREAT » Mon Jan 14, 2008 6:10 pm

Hotwired wrote:I'm a big fan of practical results so most theories going past me get a pinch of salt.

A 16g dart from a 1200mm x 20mm barrel @ 3 degrees with a chamber of say 1000mm x 20mm of 450psi air behind it to go 500m...

...is certainly pushing the boundaries of what I consider likely.


As a practical and negatively optimistic type, what I'd expect when in field conditions is for a high speed dart at that angle to zip into the ground significantly short of 500m and require a metal detector to find it again.

I'm open to being proved wrong by the ultimate test of a physical demonstration though.


maybe a picture or diagram of said dart would help for two reasons 1) so i can copy it 2) it might help prove us wrong.

edit: i just did some reaserch into the power of .22LRs and i found that my 20mm porting piston gun will have considirably more power :twisted: although thats only to be expected with a 20g steel ball :roll:
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