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Stock Micro Dart Physics

Is weight an issue in range?

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#1 Raj Man

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Posted 31 May 2006 - 02:24 PM

I have searched this website and googled about these questions, but here they are:

First: Scientifically, what is the MAXIMUM physical range that a stock micro dart can fly after being fired from a very high-power gun? :wacko:

Second: How much does weight affect the range and flight of stock micro darts?

Thanks in advance for any answers to the above questions!
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#2 blinkycc13

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Posted 31 May 2006 - 02:51 PM

Weight of something does not affect how fast it falls. Everything falls at an acceleration of approximately 9.8 meters per second in a vacuum. Air provides some resistance.

To increase distance, you need to increase power or decrease friction. Therefore, I suppose the maximum range is whatever you can get with the largest amount of power before the dart starts burning up due to friction with the air. I doubt anybody actually knows what this distance is.

edit: FH: True, inertia favors small objects. However, the less mass a dart has, the less momentum. The ideal dart would be small but also somewhat dense so that it has momentum. Also, thos would be extremely inaccurate(sp?)

Edited by blinkycc13, 01 June 2006 - 03:02 PM.

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#3 Flaming Hilt

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Posted 31 May 2006 - 03:35 PM

Weight of something does not affect how fast it falls.


That is true.

However, the weight of something does affect its inertia. The more it weighs, the longer it takes to accelerate (neglecting ballast and uh... being like a feather). For example, try throwing a really big rock and then a really small one. It is true that they will fall at the same rate, but you won't be able to throw the big one as far because it has more inertia. The same is true for darts.

So, I guess the perfect weight for a dart would be as small as possible, but still enough to not [be a feather] (sorry I can't remember what that word is...).

Edited by Flaming Hilt, 31 May 2006 - 03:36 PM.

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#4 AssassinNF

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Posted 01 June 2006 - 01:56 PM

The weight of a dart should be directly proportional too the power of the gun it is fired out of. If a dart it too light, it spins off course in mid air and drops right in front of you (ever tried firing an un-weighted stefan?), and if it is too heavy, it just drops the second you fire it.

For example, a singled titan can fire very heavy darts, and sometimes stock darts will spiral out of control when fired out of it, where a smaller gun can fire lighter darts with no problem.

Weight of something does not affect how fast it falls.



That is true.


That is only true in a vacuum, as air resistance slows down objects. Drop a feather and a bowling ball at the same time... you can't say that they fall at the same speed. Heavier darts can achieve greater ranges with enough power than lighter darts can, because air resistance has less effect on them.

And inertia... it is true that because of inertia, heavier objects take alot more force to move, but it is also true that while they are moving, it takes more force to stop them. This enables heavier darts to achieve greater range and accuracy because of the extra momentum.

I think the maximum for a stock dart is probably around 150'-200' before the gun is so powerful that the darts start being shredded...

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Edited by AssassinNF, 05 June 2006 - 02:07 PM.

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#5 ntietz

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Posted 01 June 2006 - 02:15 PM

That is only true in a vacuum, as air resistance slows down objects. Drop a feather and a bowling ball at the same time... you can't say that they fall at the same speed. Heavier darts can achieve greater ranges with enough power than lighter darts can, because air resistance has less effect on them.


In a vacuum or on earth, if you drop two objects with the same surface area and shape, they will fall at the same rate regardless of weight. If you don't believe me, try this: Take two bowling balls and fill the holes of one with lead, and fill the holes of the other one with... say... foam, then cover both of them with duct tape so the outer surface is the same. They will fall at the same rate.
The reason that feathers and bowling balls don't fall at the same rate is because feathers have a much less aerodynamic structure and are more wind resistant.
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#6 AssassinNF

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Posted 01 June 2006 - 02:44 PM

True.... comparing a bowling ball/feather to two different darts wasn't a very good analogy, but we are talking about shooting darts, not dropping them. :)

Edited by AssassinNF, 05 June 2006 - 02:10 PM.

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#7 Nero121

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Posted 01 June 2006 - 03:50 PM

Or, so that you could avoid the bowling balls, you could use a big marble and a bouncy ball. Anyway, does this mean that it would be better to make heavy darts for a Titan? Would that get more range?
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#8 userjjb

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Posted 01 June 2006 - 07:21 PM

OK, I'll try to clear things up here, as there is a lot of confusion of terminology.

In order to predict the motion of an object, you need to consider all forces acting on the object, as well as the object's initial state. It is as simple as that. In our discussion here there will be two forces acting on the dart, gravity and friction.
----------------------------------------
To start off simple, let us imagine the dart in the ideal conditions of a vacuum. Here there is only one force, gravity, and the analysis of the motion of the dart is quite simple. The dart emerges from the barrel with some initial velocity v at a height h. For simplicity, let us assume it emerges from the barrel parallel to the ground.
Now lets resolve the forces. For our purposes we don't necessarily need to consider the force of gravity, but rather the acceleration due to the force of gravity, which at the earth's surface is 9.8 m/sē. Using an accepted formula d=gtē, solving for t we get t=√(h/g). At a height of one meter, this is roughly .3 seconds.
Now that we know the flight time, we can substitute this in a simple distance equation: d=v/t. The v is the velocity of our dart and t is our flight time. Thus, for a dart fired at 1 meter off the ground, the distance traveled will be v/.3 where v is the muzzle velocity in meters per second.
So for example, if you fire the dart at 6 m/s, it will travel 20 meters.

First: Scientifically, what is the MAXIMUM physical range that a stock micro dart can fly after being fired from a very high-power gun? :)

Second: How much does weight affect the range and flight of stock micro darts?

As you can see, in a vacuum a dart has no maximum velocity, nor does it's mass affect its range. However in real world conditions things are different, both of these answers will change once we factor in drag forces.

I only had a little bit of time to do this post. In a day or two I'll add a second part, adding on the effect of drag forces on the dart's motion.

Edited by userjjb, 01 June 2006 - 07:50 PM.

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#9 Flaming Hilt

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Posted 01 June 2006 - 08:27 PM

Heavier darts can achieve greater ranges with enough power than lighter darts can, because air resistance has less effect on them.


Nuhuh...uh...hmmm...

*thinking...*

I dunno. Weight is inertia but I don't think just because something is heavier it has less air resistance. Take a feather and a BB for example (I know a BB is prolly still more weight than a feather, but it's better than a bowling ball). The air resistance has to do with the surface of the item. Two darts, one heavier than the other but still with the same surface would still get the same air resistance: unless you change the surface when making one dart heavier, there is no difference.

I agree that heavier darts have more inertia thus taking longer to slow them down, but the point I was getting at was it would be harder to acclerate them -- you'd need a bigger gun. Sticking with the same gun, less weight is better. As soon as you make a gun with more power/acceleration/etc. (longer barrel or more pressure), go ahead and make a heavier dart because then you can accelerate it more.
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#10 blinkycc13

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Posted 01 June 2006 - 09:40 PM

Heavier darts can achieve greater ranges with enough power than lighter darts can, because air resistance has less effect on them.



Yes, heavier darts will acheice greater ranges with enough power than lighter darts. Assuming that the darts are the same aside from density, then air resistance will be the same. Air resistance will take longer to "work," as the dart's momentum works against the air resistance. So, momentum seems to be important, as long as the darts are same size, etc.

Edited by blinkycc13, 01 June 2006 - 09:41 PM.

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#11 Meaker VI

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Posted 01 June 2006 - 09:53 PM

I dunno. Weight is inertia but I don't think just because something is heavier it has less air resistance.... The air resistance has to do with the surface of the item. Two darts, one heavier than the other but still with the same surface would still get the same air resistance: unless you change the surface when making one dart heavier, there is no difference.

...Sticking with the same gun, less weight is better....


First, weight is part of inertia, the other part of inertia being velocity. For example, a dart is stationary and has stationary inertia, it doesn't want to do anything. To make it move, you must exert force on it, but once it gets moving it has moving inertia and doesn't want to stop. Inertia is the desire for matter to keep doing what it is doing, to put it non-scientifically. Air resistance is another thing entirely, and it has to do with surface area (like you said) and mass, which is weight per volume. Two darts can be the same weight and different sizes (take a micro and a mega that weigh the same), the smaller dart will travel farther (why most people use micros now).

And the second statement is not nessecarily true. Someone posted earlier about a Titan shredding lighter darts; heavier ones are nessecary. Finding the optimum dart doesn't always mean picking the lightest one since the heavier ones have more inertia and that helps with drag. I'm sure userjjb will explain all that better than I can.

Edited by Meaker VI, 01 June 2006 - 09:55 PM.

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#12 Master Yogurt

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Posted 01 June 2006 - 10:57 PM

Also, because of the mass of heavier darts, they are harder to throw off course. A lighter dart will suffer greatly from wind, but a heavier darts will sail truer. Other people have already gone over the physics of the matter, so I won't go into it, really. Still, I don't believe that it's really possible to fire a dart (especially stock) more than 150-200 ft. They're only SO durable, and even if you could achieve more, I don't believe that the darts would be able to stand that for more than a couple of firings.
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#13 Carbon

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Posted 02 June 2006 - 11:49 AM

Still, I don't believe that it's really possible to fire a dart (especially stock) more than 150-200 ft. They're only SO durable, and even if you could achieve more, I don't believe that the darts would be able to stand that for more than a couple of firings.


Or even one. Stock darts tend to explode with an extreme blast of air...an AT2k has enough power for that. You can improve durability by shoving a drinking straw into the hole in the dart.
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#14 AssassinNF

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Posted 02 June 2006 - 09:06 PM

Reading my own post showed me alot of crap that I didn't even know I typed ;).... anyway, my main point was that more powerful guns need heavier darts, and weaker guns need lighter darts.

When I said air resistance has less effect on heavier darts, I meant to say that heavier darts are less affected by wind/drag and are harder to blow off course because of their momentum, as Master Yogurt mentioned. Oh well, my bad.

I apologize for anything in that post that was really off. :blush:

Edited by AssassinNF, 05 June 2006 - 02:09 PM.

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#15 userjjb

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Posted 02 June 2006 - 11:59 PM

OK, sorry I couldn't explain the more real world case right away, I had to do some calculations.

This next model takes into account the second (and more complex) force on the dart, air drag.

A little explanation of air drag will go a long way to hopefully illustrate how exactly it works. The formula for the force due to drag is F=1/2 p vē A Cd, where p is the density of the fluid medium, v is the velocity of the projectile, A is the reference area of the projectile (imagine a slice through the dart perpendicular to the direction of travel). and Cd is the coefficient of drag (it's a dimensionless number related the shape of the object). I'll save you the drudgery of calculation, for a 1 cm diameter dart, F=.1 vē roughly(in units of g*m/sē).

Here's where things get interesting.

One problem in calculating how drag force affects the dart velocity lies in the fact that it is dependent on the dart velocity. Drag slows the dart, which in turn changes the drag force in turn affecting dart velocity. This would normally be a job for integrals, however since the time of flight is relatively short, the drag force is "relatively" constant. (Go ahead and feel free to do out the integrals for the time dependent velocity function if you want, for our purposes the accuracy is unneeded and my approximation is sufficient.)

Now that we have the force, we can calculate the deceleration due to drag using Newton's formula of F=ma. a=F/m where F is the drag force and m is the mass of the dart.

Resubstituing the newly found drag deceleration into our formula along with a little creative rearrangement of terms we get:
d= v/t - .1vē/m


This formula actually came out better than I thought it would, the first term v/t is exactly what we had before in my first post. The second term modifies this, subtracting from the total range based on it's mass and velocity.

Looking at the second term, one can now clearly see the effect of the mass of the dart on range, the greater the mass of the dart, the farther it will go, up until a limit. It is important to note that this isn't a one to one ratio, if you double the weight of the dart it isn't going to go twice as far. Dart weight's effect is only noticeable if the dart is too light, or the dart velocity is high.

We can also answer the other question about a maximum dart range, short answer:no. Long answer: In order to achieve greater dart ranges, we need to increase the muzzle velocity of the dart. This isn't a problem at first, however we soon encounter a technical difficulty. The drag force is proportional to the square of the velocity, whereas it's directly proportional to the mass. This means as we increase the dart velocity we will have to increase dart mass exponentially. However, as long as you have a potent enough nerf gun, and resilient enough darts, there is no maximum range.

Before I end let me say a couple of things though. This post was intended to explore the motion of a dart through the air, exploring the effect of it's mass, as well as determining if there is a theoretical maximum range. There is still the consideration of the flight characteristics of a dart, as well as the method of propulsion to consider. Hopefully this has been helpful.

Edited by userjjb, 03 June 2006 - 12:01 AM.

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