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We Report Range, Why Not Velocity?

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#1 Guest_TheSilverhead_*

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Posted 01 November 2010 - 09:02 PM

OK, preamble time! In our various modifications, we always either report range or be highly doubted. Now, I have rather found this misleading. For example, I did a fairly decent raider mod for indoor wars, and got decent range. However, once in war, a rather lithe friend of mine dodged every dart except my shotgun. Now, I tried to figure out why this was. Of course, the answer was VELOCITY.
Consider this highly exagerated example: Cpt. Slug makes the Nerf equivilant of a cruise missile- shall we say 200 foot range, high accuracy, perfect speed so it doesn't kill small children. The catch- it takes say 8 seconds to travel this 200 feet, so we have high range, low velocity. Of course, unless Slug also makes a guided dart, this ain't gonna work.
Now, on the other extreme, FA_24 makes a gun that acheives maximum range in an inmesurably short amount of time. This gun's catch: 20 foot range, E.G. high velocity, low range.
What does all this amount to? Well, I thought it would be a good idea to report range AND VELOCITY in our modifications/writeups. Now, I pondered over this, until I remembered a very basic physics equation. Namely, it allows us to measure velocity with no information except:
Height of muzzle from level floor
range of projectile
Everything else is constant- the force of gravity, air resistance, etc.
So, shall we say that we fire a gun from 0.45 meters off the ground. This bullet goes 81 meters. If the gun is fired at theta=0 degrees (parralel to a evel plane, e.g. floor), we have everything we need to get velocity.
First up, we will divide the unkown velocity into the X- and Y-dimensions. Since the gun is horizontal, velocity in Y=0%, velocity in X= 100% of total velocity. We will start in the Y-dimension to calculate time.

Our first equation is:
delta X= Vo (multiplied by) time (plus) {0.5 (multipled by) acceleration (multiplied by) time [2]}

Where
Delta X= displacement, or range
Vo= initial velocity (remember, this is in the Y, or vertical, dimension, so if the gun is parralel to the floor, it will have an initial Y velocity of 0)
time= duh. time in seconds.
0.5= Half of. Again, duh.
Acceleration= the downwards acceleration due to gravity, in negative. (Again, becuase this is the Y dimension, this is the only force acting upon the bullet besides air resistance.)
and time squared=time squared.
Here, [2] means "preceeding value squared", and subsequent values in parantheses ,(9)(5),means to "multiply these adjacent values", so (9)(5) would be 45

What we are doing is using the rate at which the bullet falls to find the time it takes. Neat, huh?

With our units,

-0.45 m = (0 m/sec)(T) + (0.5)(-9.8 m/sec[2])(Time)
simplified:
-0.45 m = (0.5)(-9.8 m/sec2)(time[2])

re-arranged to find time:


Time [2]= (2)(0.45 Meters)
..............____________
............. 9.8 Meters
.............___________
............. Seconds [2]

which means that

Time= 0.30 Seconds.

Phew. Next up, the X-(horizontal) dimension!

Now that we have time, we can use the same equation to get velocity!

delta X= Vo (multiplied by) time (plus) {0.5 (multipled by) acceleration (multiplied by) time [2]}

Delta X= displacement, or range
Vo= initial velocity (remember, this is in the X dimenion. This is the velocity we want to find.)
time= duh. time in seconds.
0.5= Half of. Again, duh.
Acceleration= 0. Once the bullet has left the chamber, it stops accelerating. Ignoring air resistance, since this force will be present at all times, unless someone hosts a Nerf war in space, is an acceptable allowance.
and time squared=time squared.

So,
81 Meters= (Velocty)(0.30 seconds) + (0.5)(-0.0 M/sec[2])(Time)

simplified:

Velocity= 81 Meters
............___________
............ 0.30 seconds

And so, finally, Velocity of bullet= 2.7 times 10 [2] M/sec.

thanks k9, of course, drag does cause some reduced velocity. This is average velocity, so drag is accounted.



Boom! Not bad, eh? It may seem like a lot, but I can measure, average, and calculate this in a very short amount of time. Personally, I think it is a good idea to report this, and I will be doing so in my 100th Post, when I unviel the Triple Triple Strike.

Well, What do you think? Q? C? F? Lolcats?

~The Silver Head~

Tl;Dr- GO BACK AND READ IT.

Edited by TheSilverhead, 01 November 2010 - 10:03 PM.

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#2 Hipponater

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Posted 01 November 2010 - 09:11 PM

First off, Nerf guns shoot darts, not bullets. They also don't go 81 meters.


Secondly, you're trying to make a point about a 200 feet range slow moving dart, and a 20 foot fast moving one, however, with the equations you presented, the 200 foot range would have a much higher velocity. Because of this, when someone reports a 'range', they effectively tells you how fast the darts move out of the blaster. Darts don't usually float or glide, they will always spend the same amount of time in the air when fired from the same height.
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#3 Guest_TheSilverhead_*

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Posted 01 November 2010 - 09:23 PM

Of course they don't shot bullets, or 81 meters, but the rest of that statement makes no sense. I shoot a mav. You shoot a singled titan. Which bullet has more air time? The titan's dart. I shoot off of the empire state building, you shoot from shoulder hieght, same gun. Which one has more air time? The one off of the skyscraper. Anyway, the height from which it was fired is just a variable, not a game-changing factor.
Have you worked it out? 8 seconds/200 feet= 25 feet/second. 20 feet/ 0.1 second= 200 feet/second.
It may not be vital, but it gives a better indication of the gun's performance.
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#4 k9turrent

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Posted 01 November 2010 - 09:28 PM

TL;DR

But are you assuming that there is no loss of energy due to friction?
If so, you fucked up

But good job for being able to apply your Gr 11 physics to nerf.

Edited by k9turrent, 01 November 2010 - 09:34 PM.

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QUOTE View Post

That's about it. And thanks Angela who helped me with these pictures.. It looks huge in her hands.


HOLY CRAP!

FU ALL

#5 Guest_TheSilverhead_*

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Posted 01 November 2010 - 09:34 PM

No, i did not assume this. I ignored this variable, as A) the entire calculation takes place once the dart has left the barrel, therefore barrel friction is not used. Also, as mentioned, B...) since we are not going to Nerf in space (as awsome as that would be), the air resistance will be constant, therefore the equation need not take it into account. If you ever have a bullet stop in mid flight, then drop straight down, let me know, and I will make a new euqation.
Hehe, B then parantheses is B).

Edited by TheSilverhead, 01 November 2010 - 09:36 PM.

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#6 Hipponater

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Posted 01 November 2010 - 09:34 PM

I shoot a mav. You shoot a singled titan. Which bullet has more air time? The titan's dart.

You may need to wait til tomorrow for your high school physics class (at best) to cover that two objects falling from the same height (like darts fired at no angle) will hit the ground at the same time, regardless of initial velocity, because that initial velocity is all in the x direction.


Have you worked it out? 8 seconds/200 feet= 25 feet/second. 20 feet/ 0.1 second= 200 feet/second.


Sure, if you pull those times out of your ass. However, fired from the same height, they will both be in the air for the same time.
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#7 Guest_TheSilverhead_*

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Posted 01 November 2010 - 09:43 PM

Even if the time is the same, velocity is different.
Also, oh Hippo, all initial velocity is in the X dimension, yes, but all acceleration is in the Y. Time out of my... Right. I just won't think about that. Anyway, I'm not trying to make an enemy out of you, I am defending my idea.
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#8 k9turrent

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Posted 01 November 2010 - 09:46 PM

Also, as mentioned, B) since we are not going to Nerf in space (as awsome as that would be), the air resistance will be constant, therefore the equation need not take it into account. If you ever have a bullet stop in mid flight, then drop straight down, let me know, and I will make a new euqation.


Drag (air friction)
Posted Image
*induced drag does not apply to darts*

Since:
As the speed increases, drag increases.

Therefore:
The drag is not a constant.





Ref.
http://en.wikipedia..../Drag_(physics)
I'm a fucking pilot

Edited by k9turrent, 01 November 2010 - 09:48 PM.

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QUOTE View Post

That's about it. And thanks Angela who helped me with these pictures.. It looks huge in her hands.


HOLY CRAP!

FU ALL

#9 Guest_TheSilverhead_*

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Posted 01 November 2010 - 09:59 PM

Very nice, K9.
1) I salute your service
2) The drag on a dart is small. Although the drag increases as speed does, it will not change mid-flight. Also, we will probably never hit airspeed at which drag increases would we?
3) I'm putting this in the post.
4) The equations are for average velocity, therefore drag is taken into account, right?
Thanks K9.

Edit:

The first diagram says that drag caused by a dart shape has almost no drag, but skin friction. However, skin friction is awfully low for foam, right?
Er, could you tell me how you got that image? (hosted link, etc?)
edit2: I don't want to use up my posts. 204 mph? Sheesh, that's a bit on the extreme end. Anyway, constant velocity is not what I'm calculating. it's average velocity. It may not differ much for nerfers, but the muzle velocity of a firearm is almost always reported in its specs.
I'll do some broad calculations tommorow on my arsenal to check the differences. It might be that a very small change in velocity can make a large difference in ability, so i will also do some long-term field testing. labeling the max range and velocity of my guns, then get reports of accuracy and functional range from helpers.

Edited by TheSilverhead, 01 November 2010 - 10:27 PM.

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#10 k9turrent

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Posted 01 November 2010 - 10:09 PM

http://en.wikipedia....ojectile_speeds
http://en.wikipedia....ojectile_motion

Our darts are relatively low mass and it has been noted that a single titan has clocked over 300ft/s (204 mph)

Not a good mix if you want to keep a constant speed.

Edited by k9turrent, 01 November 2010 - 10:19 PM.

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QUOTE View Post

That's about it. And thanks Angela who helped me with these pictures.. It looks huge in her hands.


HOLY CRAP!

FU ALL

#11 Doom

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Posted 01 November 2010 - 11:33 PM

TheSilverhead, I appreciate the effort, but I'm afraid that you don't know enough to properly characterize this problem.

As has already been said, drag is not negligible. Including drag in a simple equation for range is also not trivial, but I did it months ago. Be aware that I provide no derivation for the second equation there. It was found via curve fitting to data generated from a dimensionless numerical simulation (i.e. something that is way above the heads of basically everyone here but me).

You can use this to get an estimate for muzzle velocity.

If you are serious about muzzle velocity, however, you should use a chronograph as I do.

Drag is not a constant or small for a Nerf dart (the drag coefficient of a Slug dart is about 0.34). The problem with high Reynolds number drag is that the approximate equation for it is non-linear (see Wikipedia), which means in this case that there is no analytical solution to the differential equations governing projectile motion. This is why I used a numerical simulation to generate data that I later fit curves to.

Average velocity does not take into account drag. I don't even know what you mean by average velocity TheSilverhead. (After Split explained it, I get it now.) To take into account drag in a simple sense, one must start with the conservation of momentum, Newton's second law, and the drag force equation.

All of the above can be learned in a few classes/books/internet websites about classical mechanics, fluid mechanics, and differential equations.

Edited by Doom, 03 November 2010 - 08:24 AM.

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#12 Zorns Lemma

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Posted 02 November 2010 - 02:24 AM

I shoot a mav. You shoot a singled titan. Which bullet has more air time? The titan's dart.


Actually, they have almost the same air time. *raucous buzzer noise*
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#13 Lion

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Posted 02 November 2010 - 03:00 AM

I shoot a mav. You shoot a singled titan. Which bullet has more air time? The titan's dart.


Actually, they have almost the same air time. *raucous buzzer noise*



this all goes back to a bullet droped vs a bullet fired, something physics says is true but no one really did it, if anyone watches mythbusters, they fucking did it and showed that physics is right
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#14 Buffdaddy

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Posted 02 November 2010 - 03:31 AM

2 thoughts:

1) Bring it to a war and shoot it.

2) Video.

Those are by far the best ways to express range/how hard it shoots.

Personally, when I'm at a war, my first consideration going after someone is never going to be "Will my dart travel fast enough", but "can I reach that far".

Foam is foam as far as I'm concerned, and aside from considering the difference in flight between slugs and glue domed darts, I'm just going to guess how much I need to lead my shots and go for it. If I miss, fine. Nerf isn't so serious that we need to take the rotation of the earth into account, for goodness sake. Just shoot the damn things and laugh at your titanic failures.
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#15 Draconis

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Posted 02 November 2010 - 10:50 AM

Also, as mentioned, B) since we are not going to Nerf in space (as awsome as that would be), the air resistance will be constant, therefore the equation need not take it into account. If you ever have a bullet stop in mid flight, then drop straight down, let me know, and I will make a new euqation.


Drag (air friction)
Posted Image
*induced drag does not apply to darts*

Since:
As the speed increases, drag increases.

Therefore:
The drag is not a constant.


I don't know, this is pretty much a constant drag.



I'm a fucking pilot


Is that like porn in the air?

Anyway... Another big problem with just reporting muzzle velocity is that the range will vary quite a lot with different darts. Even if they all were the slug design, with the same dimensions, small variation in the mass of the washers used will change the range dramatically. Beside that, measuring velocity is substantially more difficult, unless one has a chronometer. Which most of us don't. But nearly all of us do have a section of sidewalk or yard that we can measure out and shot along.


Oh, and another thing. THEY ARE DARTS, NOT BULLETS.

Edited by Draconis, 02 November 2010 - 10:58 AM.

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[15:51] <+Noodle> titties
[15:51] <+Rhadamanthys> titties
[15:51] <+jakejagan> titties
[15:51] <+Lucian> boobs
[15:51] <+Gears> titties
[15:51] <@Draconis> Titties.
[15:52] <+Noodle> why is this so hard?

#16 Guest_TheSilverhead_*

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Posted 02 November 2010 - 12:03 PM

haha, I see what I mistyped. By airtime, I didn't mean different times in the air, or hangtime. I meant to type air/time, or distance/time, not saying that a faster DART spends longer in the air. Alright, 'll change all bullets to darts, but what if you fired from X height (shoulder) and instead measured the drop of the dart at optimum operational range? This would give you the velocity over the useable span of its flight. I'll update the first post when I get back from tutoring.(I'm the tutor, not the student. A birthday doesn't tell you what grade you;re in, now does it?)
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#17 Zorns Lemma

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Posted 03 November 2010 - 05:24 AM

If I add dart/time to air/time will I finally have bullet/time?
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#18 Split

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Posted 03 November 2010 - 05:54 AM

Your intentions are good, and you're right that the "average velocity" does include drag, but that average velocity is virtually useless. What we're looking for is muzzle velocity. Because average velocity only depends on the distance traveled (assuming angle and height are the same, which they typically are), reporting both the distance traveled and the average velocity gives no additional information. Reporting the average velocity instead of range would simply be more inaccurate, as it magnifies any error or outlier or rounding.

As for the drag itself, it is actually a very noticeable force, especially right out of the barrel as it moves quickest. If you want the (useful) muzzle velocity, your best bet is to use a chronograph, as Doom suggested. A few of us have used them in the past, but they're too expensive to be practical for widespread use.

It was found via curve fitting to data generated from a dimensionless numerical simulation (i.e. something that is way above the heads of basically everyone here but me)

HeyHeyHey!

Edited by Split, 03 November 2010 - 09:16 AM.

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Teehee.

#19 sublimedom777

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Posted 03 November 2010 - 08:49 AM

Darts don't usually float or glide, they will always spend the same amount of time in the air when fired from the same height.


You've never had a breeze mess with a shot, and all your blasters shoot the same range every time? Man, all we might as well give up, this guy is too lucky and too good.



Kudos on trying to apply physics Silver.

Anyway, as said, the sheer simplicity of laying out a measuring tape and reading a few numbers is way better than mucking about with units, calculations, conversions, girls, math, and other things 13 year olds can't do.

How about we all go back to having fun shooting foam projectiles around now?
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#20 Guest_TheSilverhead_*

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Posted 03 November 2010 - 12:27 PM

Ah, for the want of a vacuum chamber. In space. Alright, thanks for all the feedback. I guess I'll get back to that homeade backpressure release valve now.
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#21 imaseoulman

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Posted 03 November 2010 - 05:50 PM

Can anyone explain how we've filled two pages to say that the faster the dart leaves the barrel the farther it will go? Or has Aristotle been right this whole time?
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#22 Lion

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Posted 03 November 2010 - 06:06 PM

Can anyone explain how we've filled two pages to say that the faster the dart leaves the barrel the farther it will go? Or has Aristotle been right this whole time?




Some members don't beleive that because they only angle their nerf blasters when recording range.
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#23 Y-Brik

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Posted 03 November 2010 - 08:09 PM

If we're looking for a more accurate way to determine a blaster's power, just shoot straight up. Time how long it takes from launch to landing, and you can work out the physics in that way. Or just do what the rest of us do and measure out your range with a tape measure.
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As I said I have not not alot of testes yet but I will be once I finish the mod.

Why I am boycotting Hasbro

#24 Guest_TheSilverhead_*

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Posted 03 November 2010 - 08:47 PM

Again range is one thing. This may not be the way to calculate it, but velocity is a very imprtant factor, if it can be accurately reported and applied. Go look at any pack of real live gun ammunition- range AND velocity is always reported. Still, the Aristotle refernce wasn't needed.
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#25 Y-Brik

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Posted 03 November 2010 - 09:36 PM

Here's the thing you're missing- range is a FUNCTION of velocity. Acceleration due to gravity (Ag) is constant regardless, so what our blasters are doing is propelling these darts to move away from us as fast as possible so that it can cover a lot of horizontal distance in the largely consistent amount of time it takes for the dart to drop straight down. The slower the dart, the less range it covers before gravity pulls it to the ground, etc.
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As I said I have not not alot of testes yet but I will be once I finish the mod.

Why I am boycotting Hasbro


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