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How to work out ACCURACY & RANGE at the same time (Read 9290 times)
JudoP
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Re: How to work out ACCURACY & RANGE at the same time
Reply #30 - Sep 11th, 2017 at 3:14pm
 
Air resistance complicates things a lot, but we can use calculations with no air resistance to set limits (no spin effects either- though I suspect these would be comparatively small).

The maximum range of a projectile on flat ground with no air resistance is given by:

R=(v^2)/g

R: range in meters
v: Launch velocity (magnitude of)
g: Gravitational constant 9.81 m/s^2

By using this formula you can set theoretical maximum range per initial throw velocity, or a theoretical minimum throw velocity (and therefore muzzle energy if projectile mass is known) for a given range.

Launch speed - maximum possible range

10m/s  -  10m
20m/s  -  41m
30m/s  -  92m
40m/s  - 163m
50m/s  - 255m
60m/s  - 367m
70m/s  - 499m
80m/s  - 652m
90m/s  - 826m
100m/s- 1019m


Range - Theoretical minimum speed

50m -  22m/s
100m - 31m/s
150m - 38m/s
200m - 44m/s
250m - 50m/s
300m - 54m/s
350m - 59m/s
400m - 63m/s
500m - 70m/s
600m - 77m/s
700m - 83m/s
800m - 89m/s
900m - 94m/s
1km   - 99m/s

The ranges and speeds above are essentially the 'correct' answers if air resistance (and spin effects) were none-existent.

For example it is physically impossible to throw 200m if you cannot impart an initial speed of 44m/s- and if say, your absolute highest launch speed was 50m/s then it would be physically impossible to throw further than 255m.

There is some evidence (the slinging paper) that these numbers could be relatively accurate if you are using ammunition such that air resistance is very small and has little effect (lead glandes etc). On page 79 a computational method shows lead glandes achieving 170m vs a theoretical maximum range of 187m (one could imagine tungsten glandes falling somewhere in between).

Here less aerodynamic projectiles are significantly impacted- the clay balls achieved only 105m from the same projected initial velocity, I imagine that natural stones are at best similar to this and at worst, much less- requiring far higher launch speeds than the calculated minimum (though the calculation of so is only possible with computational methods).

Also interesting is that the positive effect of using a biconical vs a ball is stronger in clay than lead- as any further improvements bring it ever closer to the theoretical maximum range.

Slinging paper: http://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1032&context=anthrothe...
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Morphy
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Re: How to work out ACCURACY & RANGE at the same time
Reply #31 - Sep 11th, 2017 at 3:52pm
 
Thats interesting. I wonder just how much spin would affect something like a Tungsten sphere. Would the spin have to increase proportional to the increase in density vs. something like a baseball?

Anyhow, very cool stuff. I have to admit I really dont understand how one releases a sling projectile without inducing spin into the throw.

The only way I can imagine is to use a mechanical release which releases the projectile without a pouch.
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Curious Aardvark
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Re: How to work out ACCURACY & RANGE at the same time
Reply #32 - Sep 11th, 2017 at 3:58pm
 
well you could do it with a pouch that opened in the middle so the missile went through the bottom of the pouch.
You're never going to get zero rotation. But a base opening in a captured pouch would be as close as you could get. 

Given that due to the variation in atmosphere density and air currents - a none rotating ball is effected much more - which is why knuckle balls move around unpredictably.
And balls with spin behave more predictably.

The atmosphere is not a single consistent medium, so no mathmatical calculation that treats air resistance as a constant can ever get close to an accurate prediction. 
Air density also varies with altitude, weather and air temperature.
Not too mention currents that act to move an airbourne object in different directions.

And yes you can throw much further in a vacumn as there is no air resistance.

It's just one reason that no slinging calculator is ever very accurate. There are just far too many variables in the real world that are different for every single throw.
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Re: How to work out ACCURACY & RANGE at the same time
Reply #33 - Sep 11th, 2017 at 5:02pm
 
Here here CA
I'm with you the theory is so dynamic with unknown variables all we can do is speculate.

Who's gronk
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JudoP
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Re: How to work out ACCURACY & RANGE at the same time
Reply #34 - Sep 11th, 2017 at 6:08pm
 
I think it's a little hasty to throw out the theory entirely...

You can provide calculations which draw conclusions based on assumptions (there are always assumptions in real life physics- but physics still works if the assumptions made correctly).

The calculation's applicability is subject to debate, not subject to being rejected out of hand.

As theoretical upper/lower limits I don't think there really is much of an argument you can make against them. The mathematical derivation is simple to do and fully detailed on wikipedia.

Using these you can therefore make fairly concrete statements like: It is physically impossible to throw 300m with 50m/s launch as the theoretical maximum for that speed is 255m. It's true there are other conceivable effects like lift from spin, and the wind which may positively affect the range, but it's still better than nothing to have a baseline- and it's quite probable such effects are negligible for lead due to it's small size and high mass. I certainly would not expect those effects to surpass the range advantage of no air resistance- it's at the very least a good 'smell test' for whether numbers are realistic.

They are not presented as realistic figures for day to day stone throwing but only idealized targets that are approached with very dense ammo streamlined ammo like lead glandes.

As I said above- stones and clay projectiles would be way off these maximums/minimums but lead and tungsten could be fairly close.
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Morphy
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Re: How to work out ACCURACY & RANGE at the same time
Reply #35 - Sep 11th, 2017 at 6:20pm
 
well you could do it with a pouch that opened in the middle so the missile went through the bottom of the pouch.
You're never going to get zero rotation. But a base opening in a captured pouch would be as close as you could get.
 

Sounds really familiar. I think TechStuff may have mentioned making something similar.
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JudoP
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Re: How to work out ACCURACY & RANGE at the same time
Reply #36 - Sep 11th, 2017 at 6:23pm
 
Morphy wrote on Sep 11th, 2017 at 3:52pm:
Thats interesting. I wonder just how much spin would affect something like a Tungsten sphere. Would the spin have to increase proportional to the increase in density vs. something like a baseball?


Lift due to spin (on a sphere) is proportional to the radius cubed, essentially proportional to the volume.

Since volume is inversely proportional to density (assuming you are using the same mass projectile in tungsten vs baseball) then the lift would be inversely proportional to the density.

Long story short, you use a projectile x times as dense then the projectile will encompass x times less volume and the lift force would be x times less.
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Re: How to work out ACCURACY & RANGE at the same time
Reply #37 - Sep 11th, 2017 at 6:38pm
 
Golf balls struck with backspin and enough velocity will travel further in air than a vacuum. The air helps by creating lift.
As does a frisbee, it doesn't require as much velocity because it's not falling as fast. Bipoint glandes can have this effect too however it's much harder to calculate and I'm no nasa scientist.
I'm not ruling the theory out completely I just think that it's too complicated for most of us to understand.

Vacuum 45• shots are a nice start point.
Working with spheres makes it easier.
But after that stuff gets much more complicated.
Aerodynamics of an object with spin, decreasing velocity in a dynamic wind environment.


For contrast try apply the same method to throwing a frizzbee.
The frizzbee went 200m but it was not going 44m/s.
And that same throw could be further of less in different wind environments.

Now I'm not saying balls of tungsten are frizzbees but I'm trying to point out that there are more factors at play.
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Re: How to work out ACCURACY & RANGE at the same time
Reply #38 - Sep 11th, 2017 at 6:42pm
 
I posted this before but someone might make use of it.
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Re: How to work out ACCURACY & RANGE at the same time
Reply #39 - Sep 11th, 2017 at 6:46pm
 
Curious Aardvark wrote on Sep 11th, 2017 at 3:58pm:
Given that due to the variation in atmosphere density and air currents - a none rotating ball is effected much more - which is why knuckle balls move around unpredictably. And balls with spin behave more predictably.


Spin doesn't any use while calculating range, because spin needs energy from that amount of energy that otherwise were given for range: From 200 Joule are coming either more range, more lift up or more "predictibility", but not 200 Joule for range + 20 Joule for predictability + 30 Joule for lift up (respect. some more range).

If the spin (or effected lift up) takes 30 Joule than only 170 Joule stays for (common) range (respectively for initial velocity). And as I said already: Even the sling is no perpetuum mobile. Not even spin you can get for or from nothing.
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Re: How to work out ACCURACY & RANGE at the same time
Reply #40 - Sep 11th, 2017 at 6:56pm
 
I appreciate it- I do know what you are getting at. My aim is squarely that the figures are useful as a baseline or starting point rather than a be all end all relation.

I suppose I would say in response that effects due to air resistance, lift, spin etc (any sort of interaction with the air) appear to- (or can be shown to) become quite small when effected on a small, dense projectile. This can be seen in computations where very dense projectiles can get near to the theoretical maximum range, or in the various formulas for fluid interactions-

EDIT: like the one you just posted. I used it implicitly in my last post to Morphy. It implies that movement due to a lift force becomes lower as the projectile becomes denser.

I would say that things like golf balls and especially frisbees are mechanically quite different in flight as there is a significant reliance on lift, which I don't think is the case for lead or other very dense projectiles (certainly not to the same extent).
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Re: How to work out ACCURACY & RANGE at the same time
Reply #41 - Sep 11th, 2017 at 7:14pm
 
No but larry threw stones not overly dense so one could speculate both ways. To say larry threw stones x far so then the same throw with tungsten goes further may not be true . It also my be. Like I said I'm no nasa scientist so I'm only speculating.
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Re: How to work out ACCURACY & RANGE at the same time
Reply #42 - Sep 11th, 2017 at 7:51pm
 
Mersa wrote on Sep 11th, 2017 at 7:14pm:
No but larry threw stones not overly dense so one could speculate both ways. To say larry threw stones x far so then the same throw with tungsten goes further may not be true . It also my be. Like I said I'm no nasa scientist so I'm only speculating.


Neither am I for sure- I'm out of practice on this stuff.

You are right it's genuinely up for debate, as transferring these aerodynamic effects into a range is not even possible to directly calculate (non-linear equations)- hence the reliance on computational methods to model the motion.

Gotta bear in mind too that Bray throwing verified 400m with a stone is just crazy far. It's pretty much the only reason I believe 700m is actually possible with super dense ammo (but you would have to be an *exceptional* thrower). I don't see any reason the advantages of lead would disappear at higher ranges/speeds. Though I can't calculate it so cannot verify it.
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Re: How to work out ACCURACY & RANGE at the same time
Reply #43 - Sep 11th, 2017 at 8:19pm
 
Larrys throw is exceptional and I'll agree that it opens the imagination to what a lead or tungsten gland would do in the same throw.However I don't think it's enough proof for a 700m throw being performed in real life.
Also I find a tiny lead glande is near impossible to find and see in the air. Tungsten would be even harder to See and find.
Happy to keep apexs record as an anomaly and stick with the more acceptable distances from 400-500m as record sling throws.


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Re: How to work out ACCURACY & RANGE at the same time
Reply #44 - Sep 12th, 2017 at 5:08am
 
I think we basically agree- for sure, it certainly doesn't constitute proof- especially when such throws have not been measured before. It's just an idea of what might be possible.

For proof there would need to be a video, and for it to be accepted as a new world record there would need to be independent verification.
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