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Let's talk about RANGE and DARTS

Physics and Aerodynamics

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#1 Blood Angel

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Posted 11 October 2012 - 01:23 PM

While there are a lot of thread about range, custom darts, stefans, dart tips, dart length, barrel length, barrel porting, barrel rifling, telescoping barrel diameters, springs, pressure tanks, airguns, and everything around/in between; there is very little information about why all of this works. All of the things mentioned are the reason the darts go farther and stay more accurate in flight.

Clearly the foam blaster community is a trial and error group. There are certain things I've noticed and would like to see explained or reasoned out.
Since the introduction of the Nerf Elite Series blaster, old streamline darts have been replaced with the new elite darts. There are blogs and videos to show that the reason the elite darts perform better than old streamline darts is because of the weight distribution and balance. Also, we know that after a certain distance/range or power the elite darts spiral or topple over off trajectory.

Which is the very reason stefans and other kinds of custom darts and dart tips were created. After a certain amount of distance/range/power, non-stock darts are a must to reach desired results. Keeping in mind that with increased springs, pressure, and what have you; more modifications are need to stabilize dart at greater trajectories.

There are a few questions that I have regarding these little known facts, and I'm sure more will arise as this thread progresses and greater minds get involved.

What is the maximum distance Elite darts can obtain before they start to destabilize?
What are the ideal lengths for darts, barrels, barrel types, at which corresponding power/distance level?

Obviously there are ratios between power and distance, accuracy and power, accuracy and distance, distance and dart length, distance and barrel length, accuracy and barrel length, accuracy and dart length, distance and dart tip, accuracy and dart tip; and many other relevant ratios. One of the more difficult things I am having problems with is measuring power.

What should be the measure of power for a blaster? psi? Wc = ∫ F*vdt? P(t) = F*v? fps?

Is it just easier to create more barrels and mess around with dart weights, lengths, and tips rather than to actually do the math?

What do we know.
1)The heavier the dart, the more powerful your blaster needs to be. Simple enough. But how much weight for how powerful a blaster? http://nerfhaven.com...=1

2)Domes are more aerodynamic and will travel farther than slugs (flat tips). Making them safe is the question. http://www.coop772.c...les/darttesting

3)Longer barrels increase accuracy, but make it too long and you risk losing velocity/distance. So, what is the optimum length? http://nerfhaven.com...showtopic=22446

4)Longer darts fish tail and spiral. What is the best length for stefans or streamlines? http://nerfhaven.com...showtopic=12595

While there are answers out there, do any of them really give solid answers? Not really. They provide useful results, but not answers to questions that will depend on the variables of your blaster. What I would like to see is a formula that everyone can use, if the variables are know about their blasters and dart. Is this a possibility?
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#2 Buffdaddy

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Posted 11 October 2012 - 01:56 PM

You're completely neglecting the propulsion system; even stock, there are differences in how well plungers or turrets seal, the level of lubrication in plunger tubes, the number of pumps before your OPV goes off, or even how fast you pull the trigger.

Barrels - different batches of the same material can have different IDs since only the OD is done to an exact measure.

The math itself - you're getting into fluid dynamics here. Dare I say more?...

We could go on, but the point stands: while you could in theory make an equation for this sort of thing, there would be so many variables that it would only be useful if everyone had identical blasters - and that's never going to happen.
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#3 Curly

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Posted 11 October 2012 - 03:23 PM

There are too many variables even when building the same gun over and over. A small bump in the PT can destroy your ranges. The only math I use commonly in nerf is rough quadratics to determine subjective ideal barrels for a certain blaster with my darts. I detailed this here in the first half of the post. You don't even need to do the math, just graph the results by hand and guess where the peak is.

Besides that, nerf is voodoo and using equations besides the one I mentioned will typically take longer than guess and check. If you want to get a specific range from a blaster, make one with an adjustable OPV or adjustable tension. What works for you might change with something as minor as humidity, so don't invest too much time into it.

Edited by Curly, 11 October 2012 - 03:24 PM.

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#4 ShaNayNay

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Posted 11 October 2012 - 03:27 PM

I see what you are trying to do and it is cute, but I have 2-4 hours combined of Physics and math each day at school, and by the end of the day I am completely sick of it. I personally would not care for mixing this stuff into a hobby that I look forward to do in my short breaks from school work.
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#5 TED

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Posted 11 October 2012 - 03:54 PM

Let's talk about sex, baby. Let's talk about you and me. Let's talk about all the good things and the bad things that may be. Let's talk about sex
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Star Wars can go fuck itself.

#6 Blood Angel

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Posted 11 October 2012 - 04:04 PM

There is much much more than that, I dare say.

The math itself is just physics and dynamics. When the dart is in the air there is aerodynamics involved. There maybe fluid dynamics if you are using the same calculations for air/gas as you would for liquids (even though liquids are more subject to gravity than gases), or are using liquids to propel your dart. But otherwise its just dynamics.

The point of focus would be when force is acting upon the dart in relation to overcoming the resistance needed to propel it out of the barrel. So the plungers, seals, trigger pull, lubricants, number of pumps, tensile strength of elastic band,pressure within tank, etc. are irrelevant if the measure of force acting on the dart itself over the time of its travel is known.

The point is that the equation is applied to raw physics on the dart at the moment the propulsion system (or propulsion force) acts on the dart. And the aerodynamics of the dart as it flies through the air.

If we take known values (data) and compare them to other know data, then patterns start to show. From those patterns and known values one could create a formula to account for unknowns. Example: I know a +bow can propel a 1.45g 3mm (plus dome tip) stefan dart 350 feet at a 45 degree angle with a 9/16" OD,0.535"ID,0.014" Wall,12" Length barrel.

If it can do that (and it can because I've seen it), then what is the measure of force acting on the dart at the moment of propulsion? These are visible and measurable knowns that can be used to calculate a variable unknown.

Obviously it won't make 350 feet all the time. But you can take an average and discount all darts out of range of one standard deviation. The links I put up already have the raw data to support something of that sort. That alone is good enough to find a ratio between force output, barrel length, and dart weight. I simply wanted to apply the findings to stock elite streamlines. That way a standard can be established in which one can say, "If force output is lower than X, then stock elite streamlines can be used." After that there can be a chart listing the force output to dart weight ratio. Barrel length and dart length are akin to range but more a factor of accuracy which is less of an issue of science and more of a dart smithing/blaster making art.

Basically everyone keeps talking about range, but range is dependent on blaster type (of course). But if the force generated to gain said range is known or calculated, then all kinds of useful information can be calculated. We can start to figure out the optimal configurations needed without having to do multiple trials.

And yes, I do know that spring applied air pressure force and pumped air pressurized applied force act differently upon a dart. Just like a bow string slinging a dart and rubber tubing pushing a dart apply force differently to a dart. But the mathematical force applied in all cases is calculated the same way.
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#7 Buffdaddy

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Posted 11 October 2012 - 04:32 PM

Let's talk about sex, baby. Let's talk about you and me. Let's talk about all the good things and the bad things that may be. Let's talk about sex


Ooooohhhh, baby!

There is much much more than that, I dare say.......
If we take known values (data) and compare them to other know data, then patterns start to show. From those patterns and known values one could create a formula to account for unknowns. Example: I know a +bow can propel a 1.45g 3mm (plus dome tip) stefan dart 350 feet at a 45 degree angle with a 9/16" OD,0.535"ID,0.014" Wall,12" Length barrel.


I hope you mean cm, first off.

Secondly, even this is very much oversimplified. Under what weather conditions? Humidity? Is this +bow akin to the International Prototype Kilogram? What is the diameter of the stefan, since that can vary, too? Coefficients of friction?

If you're just using "Force x" as the input, then technically you could make some sort of equation. But it would still end up being a one-time use b/c conditions change so freaking much. Thus why trial and error is STILL the best option.
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#8 Draconis

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Posted 11 October 2012 - 04:36 PM

Doom has already done most of this. External ballistics for sure. I know he was working on internal ballistics for air pressure tanks, but I'm not sure how far he's gotten with it.
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[15:52] <+Noodle> why is this so hard?

#9 Zorns Lemma

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Posted 11 October 2012 - 05:39 PM

The point is that the equation is applied to raw physics on the dart at the moment the propulsion system (or propulsion force) acts on the dart. And the aerodynamics of the dart as it flies through the air.


Your thesis seems to be "We can simply Nerf pneumatics to the instant where a force is applied to the dart before exiting the barrel. As long as we can measure this force, we can do some fancy stuff."

What if I told you that this force is not applied instantaneously, that it isn't constant, and that it depends on the velocity of the dart at the time? Are you willing to numerically compute the differential system required to derive meaningful results?

If you don't have experience in numerical analysis of differential equations/computational fluid dynamics/statistical mechanics, then your physics background is woefully lackluster for tackling the issue at hand. If you do, then in addition, this forum is not the place for that kind of discussion.

Anything relevant to practical nerf war can be achieved through empirical testing. Theory discussions just spawn pages of concept threads and silly ideas like "barrel volume should equal plunger volume."

Edited by Zorn's Lemma, 11 October 2012 - 05:41 PM.

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#10 Blood Angel

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Posted 11 October 2012 - 05:43 PM

Ooooohhhh, baby!



I hope you mean cm, first off.

Secondly, even this is very much oversimplified. Under what weather conditions? Humidity? Is this +bow akin to the International Prototype Kilogram? What is the diameter of the stefan, since that can vary, too? Coefficients of friction?

If you're just using "Force x" as the input, then technically you could make some sort of equation. But it would still end up being a one-time use b/c conditions change so freaking much. Thus why trial and error is STILL the best option.


I did mean cm.

If you believe the coefficients of friction (which are givens) will differ drastically from one brass barrel to other I suppose it is a big deal. I doubt it would be enough to make a significant difference. Weather conditions? Humidity? really? Come on, you are just nit picking now.

The International Prototype Kilogram is irrelevant since the desired information is the "force X" at moment of force acting on dart. Stefan diameter is only relevant to the point that it is such that it fits into the brass barrel (which info was given) and obtained those results.

I'm aiming for predicable consistency. Even if the conditions change, I fart and the dart goes 3 feet farther, it wouldn't change the amount of force that was acting on the dart at the moment of inertia. At a certain point "about" or "close enough" becomes good enough for me.

The purpose is to find a base line in which to calculate optimal configurations to shot a known dart, not calculate precise figures for the sake of obtaining a one time datum.

Once a base line has been established in which to calculate for certain variables, you can add whatever "outside" forces acting on the dart in motion all you want. I tend lean more towards "kentucky windage," myself. But even the best losers in the world need their base line formulas, in order to base their shot group. The weight of the bullet, size of bullet, the average FPS of the bullet, gravity, curvature and spin of the earth, are all knows and calculated. Factoring humidity, wind, how much CLP went into last nights weapon cleaning, the brand of 7.62mm, all that is factored into how the shot goes down, but its not calculated. The added factors of barrel friction, wet air, human error when cutting a dart to exactly 3 cm, etc. can all add up to a huge displacement of a dart. But it would reflect in the raw data of the numerous trial and error, that has already been done. So much so that "Doom has already done most of this. External ballistics for sure." I was just asking for the next step, basically.

I guess, I'm coming across kind of vague. The math isn't easy. I know that much. But I know its doable.
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#11 Doom

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Posted 11 October 2012 - 06:14 PM

Hi Blood Angel. These are all good questions. Some of them have been answered. Folks at NerfHaven tend to frown on mainly theoretical "concept" threads, so if you want to speculate, it might be best to take things elsewhere (I might suggest Nerf Engineering, a dead forum I run). Otherwise, do some experiments to test your ideas, run some computer simulations, or find some scientific studies and post after that.

Over the past 3 or so years I have done a lot of theoretical and experimental research about hobby guns, mainly Nerf and spud guns. I have compiled some notes applicable to Nerf available here: http://btrettel.nerf.../ballistics.pdf

That document is incomplete, somewhat disorganized, and full of errors, but that's how notes work. In that document I detail the theory behind a few things you mentioned, specifically ideal barrel length (for maximum energy efficiency, equations 2.99 and 2.132), range (flat, though this can be extended, in section 3.5), accuracy (in section 3.9), the effect of "heavy" (as I define it) darts (in section 2.1), and dart aerodynamics (section 3.7). I also discuss dart safety (section 4), reaction time (section 3.8), materials (section 5), air reservoirs (section 5.2), and energy efficiency (section 2) in some detail.

Unfortunately, very few experiments for Nerf guns have been performed. The few experiments that have been done have generally tested ideas that are implausible, like rifled barrels for weighted darts. I have tried hard to do my own experiments and find what experiments have been done to compare my theories against reality. Generally, the theories do decently.

Now to address some of your specific questions:

What is the maximum distance Elite darts can obtain before they start to destabilize?


Experiments are by far the easiest way to figure this out. The relevant experiments probably have already been done, though I don't think anyone's looked in scientific and engineering journals for it.

I'm not sure these experiments are so useful. It's pretty easy to make stable darts by weighting them correctly.

What are the ideal lengths for darts, barrels, barrel types, at which corresponding power/distance level?


Dart length is not so important for drag (see figure 7 in my document). But longer darts don't work so well in hoppers.

Ideal barrel length is best found via experiments, but you can get some estimates from the equations I derived. The barrel type affects this a bit by changing the friction. The pressure and other blaster characteristics matter too, but it's really complicated. Computer simulations calibrated by experiments are the best we can do to predict performance.

What should be the measure of power for a blaster? psi? Wc = ∫ F*vdt? P(t) = F*v? fps?


Muzzle kinetic energy, that is, 0.5 * m * v^2 where m is the dart mass and v is the muzzle velocity is the best way. You can weigh darts with a postage scale and use a chronograph to get the muzzle velocity.

The heavier the dart, the more powerful your blaster needs to be. Simple enough. But how much weight for how powerful a blaster?


The more powerful the blaster needs to be for what? To get the same range? That's not true in general. Very often you can take the same blaster at the same configuration (spring draw, pressure, whatever) and improve range and/or muzzle velocity by increasing the dart mass.

The short answer is that it's complicated. Experiments and computer simulations (if that's your thing) are the way to go.

Domes are more aerodynamic and will travel farther than slugs (flat tips). Making them safe is the question.


I used to interested in making more aerodynamic darts. But since then I've realized that the dart aerodynamics are hard to improve. You can look at figure 7 of my document to see how much we have to gain in terms of aerodynamics by rounding the nose of a dart. It's a lot, but I think I could make more progress more easily improving other things. Right now it seems that you can pick two of these in terms of darts: aerodynamics, safety, and durability. We should work on this.

Longer barrels increase accuracy, but make it too long and you risk losing velocity/distance. So, what is the optimum length?


Actually, unless your barrel is so short that it doesn't hold the dart right, barrel length has little to no effect on accuracy how you seem to be thinking about it. The reason is simple: once the dart leaves the barrel, how it moved in the past is irrelevant if you know its current position and velocity. It's not like the barrel holds the dart straight or anything. (The magnitude of the dart muzzle speed does affect accuracy, though. And this is controlled largely by the barrel length. Faster and more consistent speeds are better. But I don't think this is what people mean when they say longer barrels are more accurate.)

If you use sights you can aim more precisely with a longer sight radius (which could come from a longer barrel), but I don't think that's what you were writing about. Strictly speaking, you don't need a longer barrel to increase sight radius. Also, almost no one uses sights in Nerf, though perhaps they would benefit if they did.

Edited by Doom, 14 October 2012 - 07:56 AM.

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#12 Blood Angel

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Posted 11 October 2012 - 06:36 PM

Thank you so much for your reply.

I'm about halfway through your 54 pages of notes. It does answer a lot of what I was looking for.

Applied, experimental, and theoretical physics are what the are. I understand the frown towards concepts a lot more after this thread.

I will be sure to use the information to good use.
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