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Calculation of speed of the shaft on some distance

Thread Status: Hello , There was no answer in this thread for more than 60 days.
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tromic

Well-Known Member
Aug 13, 2007
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There is an excel file attachment based on my real measurements in water in years 2011. and 2012. I suppose it might be useful to calculate the real speed of the shaft on some distance in water for several cases: for 7/1003 mm 301 g shaft and for 8/1280 mm - 483,5 g shaft. Both shaft using two mono line thickness 1 mm and 1.5 mm. For 7/1003 mm 301 g shaft, there is also calculation/measurement for 2 mm original black Mares rope (I suppose it is maybe similar to 2 mm Dyneema)
Calculation in https://forums.deeperblue.com/threads/calculation-of-initial-speed-and-energy-of-the-spear.114778/ can be used to determine the Initial speed of the shaft.
That initial speed v0 is then multiplied with normalised speed v/v0 from given tables or using formula for v/v0 = y from the graph as on image. "x" in formula is a distance in (m) for which you want to calculate the speed. The graph starts with distance 0 m. That distance is actually measured from the shaft tip after the shaft is inserted into the spearguns muzzle before loading the speargun.

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One more thing, also very important, that influences the performance is the kind of slider on the shaft. This measurement were taken using Tomba10 slider. It was 10 mm OD slider for 7 mm shaft.
If using free shaft, mode of tying the line to the shaft also makes significant difference. Measuring 8 mm shaft performance was as "free shaft" (I was using Cyrano 1100 for shooting the spear https://forums.deeperblue.com/threads/measuring-speed-of-the-shaft.91007/page-5#post-887541 ).
I have to say, to be quite correct, I have not really tested the performance of 8 mm shaft in water using that black nylon rope because I knew it would be very poor and that I would be never using it. Formula on a graph y=e(-0,3x) for that case is result of some mathematical extrapolation combining data from 7 mm and 8 mm shaft measurement. So it should be taken having that on mind! I had really tested that black nylon line only with 7 mm shaft so that data must be correct.
 

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Bad news for Diving Gecko (Davide) end his Mirage Evo, as could be calculated from diagram above or excel file, is that even for initial speed v0 = 44 m/s (that is 33 bar/loading effort 45 kgf) using 2 mm Dyneema, speed on 5 m would be only about 10 m/s. I actually got 9,6 m/s with 483 g spear. His spear is 570 g so it would be somewhat more. On 4 m about 14 m/s. If using 1,5 mm mono speed on 5 m would be about 20 m/s.
This is just en estimation but might be very close to real situation...
 
Your calculations are wrong, a "Mirage" can shoot faster than that if you open up the power regulator block. Similarly a 13 mm diameter barrel "Sten" can shoot at high velocity when at high start pressure and can pull out three line wraps and still be able to jerk the gun in your hands when the spear tail stop hits the end of the shooting line. As a yardstick I can compare this with my "Black Sea" gun which is even more powerful.

I might add the "Sten" gave this performance with a woven nylon shooting line, the only change from normal was a low drag piston, in fact the original "Sten" back to back cup seal piston that was of all metal construction. The only reason I don't use that piston is the single rubber seals are no longer available, which is a pity as I have two of those pistons. You can see this piston without its seal in these photos.
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Bad news for Diving Gecko (Davide) end his Mirage Evo, as could be calculated from diagram above or excel file, is that even for initial speed v0 = 44 m/s (that is 33 bar/loading effort 45 kgf) using 2 mm Dyneema, speed on 5 m would be only about 10 m/s. I actually got 9,6 m/s with 483 g spear. His spear is 570 g so it would be somewhat more. On 4 m about 14 m/s. If using 1,5 mm mono speed on 5 m would be about 20 m/s.
This is just en estimation but might be very close to real situation...

Since I haven't tested my gun in a controlled setting (pool) I can't prove that it would shoot faster. My gut feeling is that it would. Most of my guns can shoot four full wraps of line, though I now rig them with three as that is all that is needed and there's a pretty nice tug at the end line when shooting.
Anyways, I hope to get a chance someday to really test this gun in a pool and then I will let you know.
We all know that the shape and size of the slider and the shooting line and its size and mass has a lot to say in how powerful a shot ends up being.
Unless I start shooting really big fish at close distances, I don't see myself using anything bigger than 1.7mm stiff dyneema or 1.7mm cable.
On one of the shafts, I initially used 1.4mm stiff dyneema but changed it out for 1.7mm later and I could actually tell a difference in shaft speed, but a medium sized doggie or GT could probably have cut the 1.4mm.
 
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Davide, what is the distance for 3 wraps for your Mirage Evo?
I suppose if using 1.7 mm Dyneema, shooting would be significantly better than with what I used in my measurement - black mares nylon rope.
I have results for 1.5 mm mono. That is better in performance than 1.7 mm Dyneema but it should not be much worse..
Have you try to use excel file I attached?
 
Once a shaft leaves a gun the gun itself is irrelevant except for the shape of the spear tail and how the line is attached to the shaft. Band guns have the shaft attached to a rear shark fin or a transverse hole in the rear of the shaft tail, while pneumatic guns and their derivatives use a slide ring as do some band guns. The difference here can be varied by changing shooting line diameter, the slider profile and maybe the shape and profile of the spear head. As the spear has to skewer and hold a fish then not a lot can be changed there. The role of the gun can be summarized by the muzzle exit velocity and the flight line of the departing shaft, the latter ideally travelling on the same axis as the gun until gravity begins to make the projectile fall and water resistance slows the shaft down, as well as drag on the shooting line.

In a pistonless gun nothing supports the shaft tail as it flies along inside the gun, so a very long gun could whip the tail before it gets out of the muzzle, however most the guns made are short and less than a meter long. A pneumatic or hydropneumatic gun controls the shaft tail with the inner barrel during spear travel inside the gun and the muzzle centralizing washer also keeps the shaft on line so that the shaft has little chance to bow as it is driven from the gun.

Band guns have no such control unless the shaft stays in the guide track and the band pull side to side on the wishbone stays the same. Since sear box mouths have become less restrictive and the shaft tail has little control surfaces acting on it, and sometimes none, the directional stability of the shaft out of these guns can be a lottery.
 
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Have you try to use excel file I attached?

Allow me to share an anecdote from the world of F1. A few years back, after a fairly big regulations change, Red Bull was tipped to come out strong. After all, they have Adrian Newey heading the design and he is widely regarded as the best aerodynamicist in F1. But when launched, the car was a lot slower than anyone expected and it was puzzling. For the first few months, nothing they did helped, new parts didn't work as they thought they would. Turned out, there was a correlation problem between their computer simulations, their wind tunnel and what they found when the car was actually out on track. (Once they sorted it out and started making up for lost time it was too late to be a championship contender, though they did pick up some wins and podiums later in the season).

Of course we are very, very far from designing race cars but honestly no, I haven't tried your excel sheet yet. And it is not because I don't care about calculations as the Russian Troll assumes.
It is for two reasons; I am a bit busy with non-spearing things but mostly it is because I don't have much need for theoretical values at this point. As long as I can not correlate them with real world testing, to me they don't have much value.
Once I have plenty of time in a pool with a rigorous test setup, it could be interesting to try to build correlation between that and the "computer simulations" aka your spreadsheet.
(One thing that might be interesting in terms of the calculations would be to compare the energy at different distances of different thicknesses of shafts being shot from the same gun at the same pressure).

On a related note, The Troll stated that I had wasted nine months on my latest build since I had not bothered to do any calculations ahead of setting out to make the gun. This is nonsense, of course, since no one can tell me how many Joules are needed to penetrate, say, a 20kg dogtooth tuna at 4m...
So, even if I had done calculations, it would have been impossible to set a meaningful design target.

On my most recent build, I set out to make the longest gun I could with a readily availiable shooting barrel. This would give me a gun 20cm longer than my previous one. With a few smaller improvements, I knew I would get a more powerful gun than the one before it which is all I needed to know at the time. I guess I could have calculated how much more powerful the new gun would theoretically be compared to the old one, but again I didn't have a need to do that. Even if the calculations would have shown the step up in power to be negligible (which I don't think would be the case), I would still have made the gun to try out 3D-printed parts and the new Mares handle.

Now, please don't think I am disrespectful of your work. It is just that where I am right now, sticking my head into other rabbit holes would pay off better - like figuring out how to make a DIY cuttlefish shaped CF barrel that can stand 40 bar of pressure or making a lever type pneumatic pump.
 
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Thanks for the interesting anecdote Davide!
But there is no any connection to this case Davide.
What I gave you is not a computer simulation!
The purpose of excel file is not to simulate anything. There are just mathematically and graphically presented data from my real measurements in sea water in years 2011. and 2012. I wrote it clearly at the beginning of the thread. Obviously you are pretty busy last days so you did not read carefully what I wrote (neighted Pete did). Presented data in excel spreadsheet have nothing with the design or brand of particular speargun. A speargun was just a tool to launch the shaft with some initial speed. I had measured that speed in several points (at least 5-6, few times for each) along the shaft trajectory and finally put that data in excel spreadsheet to analyze them through graphs. Formulas in graphs are just a mathematical tool to describe that graphs after the graphs were generated from input data - actually real measurement data.
I was interested only in shooting performance of two different shafts: 7 mm and 8 mm and the influence of different lines: 1 mm mono which I mainly use here in Mediteran and 1,5 mm mono. I also tested the original black nylon rope (2 mm?) I got with my Cyrano when I bought it because I was very disappointed with the overall shooting performance using it for the first time. It was like a slow motion film...
I have to say, to be quite correct, I have not really tested the performance of 8 mm shaft in water using that black nylon rope because I knew it would be very poor and that I would be never using it. Formula on a graph y=e(-0,38x) for that case is result of some mathematical extrapolation combining data from 7 mm and 8 mm shaft measurement. So it should be taken having that on mind! I had really tested that black nylon line only with 7 mm shaft so that data must be correct.
Here is an old chinese proverb: "Don't throw your pearls to pigs! They will trample the pearls, then turn and attack you."
 
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Thanks for the interesting anecdote Davide!
But there is no any connection to this case Davide.
What I gave you is not a computer simulation!
The purpose of excel file is not to simulate anything. There are just mathematically and graphically presented data from my real measurements in sea water in years 2011. and 2012. I wrote it clearly at the beginning of the thread. Obviously you are pretty busy last days so you did not read carefully what I wrote (neighted Pete did). Presented data in excel spreadsheet have nothing with the design or brand of particular speargun. A speargun was just a tool to launch the shaft with some initial speed. I had measured that speed in several points (at least 5-6, few times for each) along the shaft trajectory and finally put that data in excel spreadsheet to analyze them through graphs. Formulas in graphs are just a mathematical tool to describe that graphs after the graphs were generated from input data - actually real measurement data.
I was interested only in shooting performance of two different shafts: 7 mm and 8 mm and the influence of different lines: 1 mm mono which I mainly use here in Mediteran and 1,5 mm mono. I also tested the original black nylon rope (2 mm?) I got with my Cyrano when I bought it because I was very disappointed with the overall shooting performance using it for the first time. It was like a slow motion film...
I have to say, to be quite correct, I have not really tested the performance of 8 mm shaft in water using that black nylon rope because I knew it would be very poor and that I would be never using it. Formula on a graph y=e(-0,38x) for that case is result of some mathematical extrapolation combining data from 7 mm and 8 mm shaft measurement. So it should be taken having that on mind! I had really tested that black nylon line only with 7 mm shaft so that data must be correct.
Here is an old chinese proverb: "Don't throw your pearls to pigs! They will trample the pearls, then turn and attack you."

I remember your line tests well, probably they started my hunt to find the smallest sliders I could.

I will have to look into the spreadsheet at some point, but deep down I still feel that without my own testing and results to compare to, I don't know what I would get from knowing any results from the spreadsheet? I mean, I might get a good approximation of the speed but if I don't know if that speed is enough or not enough, then what is the use?;-). I think you might have said something on the thread about my latest gun that a certain shaft and pressure combination was very powerful, and I then said that in real life, I felt they were not powerful enough - hence why I feel the need for better correlation.
Maybe I am just still too stressed about other stuff at the moment, haha.
 
Yes you were right. I sad that 36 m/s was a nice initial speed. That was because I have very nice performance with only 33 m/s using 1 mm mono!
With thicker line especially with line that is not a mono line, you need still higher initial speed than 36 m/s to be sufficiently efficient on say 5-6 m. I asked you for your 3 wrap line length to see what would be your shooting distance app. I take that 10 m/s speed of the shaft, that would be about 15 J of energy for 300 g shaft, would be enough to neil some medium size fish. In your case with 570 g shaft it would be 25 J. Is it enough for your target pray (DOG).? I don't know.. You can maybe find out yourself. If you put your Miraqe Evo on 2 bar or maybe somewhat more (2.4) because of the friction of the piston. you would have initial speed of about 10 m/s. Try to shoot some target (body or head of a big fish) from 2 m distance out of the water, in air. You will see is if it enough to neil through the fish. If it is not, increase the pressure and try again. Then calculate the speed and the energy of the shaft with that pressure. You will have the data for your max shooting distance.
 
I changed y=e(-0,38x) to y=e(-0,3x) in excel spreadsheet. I suppose this would be more realistic for 8 mm shaft using black nylon rope 2 mm. Now it is more similar in relation to other measurements with 7 mm shafts... I had to to this because I did note make measurement for this case and do not have the real data.
Also have to remind that measurement in water for 8 mm shaft using mono 1 mm and 1.5 mm was made using free shaft with Cyrano 1100. Free shaft was tied as on the image in link above (in first post) , using a sliding loop with climax 0,9 mm to minimize the influence of this kind of tying the shaft.
My later measurements of performance of the free shaft had shown that this kind of tying is not the best. I do not recommend using free shaft with neither loop slider nor micro slider despite they are convenient.. They are not good for the highest performance.
This on the left was 2 mm black line I've got in box with Mares Cyrano 850. That line I've used for measurement. It is similar to the Spectra on the right side but is more rough.
It was difficult to measure its OD but it is about 2 to 2.1 mm?

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When you use mathematical modelling or experimental data extrapolated out to determine what some changed device will do then it can be useful as you can eliminate some design possibilities before you start. But we are not talking about multi-million dollar hypersonic airplanes, or 350 km/h racing cars, we are talking about spearguns where they are easy to build, so anything can be tried out experimentally. All shooting line and spear experiments could be conducted with a “Black Sea” gun as a test bed for shooting line, shaft weight and tip changes and this has already been done over a decade ago. The results showed thin slick line is faster through the water than woven cord lines. Testing by Niko Brummer using a marked shooting line with dots running through an optical frequency counter to give the speed at any point downrange showed slimmer shafts were faster than thicker shafts up until a certain point out from the gun, then the greater momentum of the thicker shaft took over and it was the faster downrange. Kinetic energy-wise the thicker shaft was superior from slightly closer in as here you are talking about velocity squared and the mass of the shaft. So this experimental work pretty much precluded the use of models because the trends are already known, so guns can be built accordingly. Also as shooting fish is what spearguns are all about choices need to be made for where the fish are shot. For example I use woven cord on my “Black Sea” gun because mono would be broken off in the rocky terrain where I hunt and the power of the gun means I can afford to throw some shaft speed away due to the higher line drag.

I looked at the spreadsheet and it is an interesting exercise, but that is all it is, an exercise limited by variables unaccounted for in it as is also the case with all mathematical models. Their results are dependent on assumptions made and what has been left out through incomplete knowledge or the inability to obtain modelling data to feed into the calculations. As for knots and ties it has long been known that crimps are the strongest and fastest through the water choices for securing lines and a crimper and box of crimps are essential if you hunt in Bluewater.
 
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That's right Pete. The results of calculation are dependent on assumptions made because they just summarises the results of measurements which are taken under certain conditions. I had already presented same data in time I made the measurements. This time I only presented them slightly different to be more useful. I thought that presented in this form that resultants might be useful for more people. Because they help to estimate what might be expected of some other users setup that is similar to what I was working with. My results may serve as guidepost about what might be expected. Everybody know that thinner line and heavier shaft iz better for performance but my calculations show the real numbers at least for assumptions made.
 
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Yes you were right. I sad that 36 m/s was a nice initial speed. That was because I have very nice performance with only 33 m/s using 1 mm mono!
With thicker line especially with line that is not a mono line, you need still higher initial speed than 36 m/s to be sufficiently efficient on say 5-6 m. I asked you for your 3 wrap line length to see what would be your shooting distance app. I take that 10 m/s speed of the shaft, that would be about 15 J of energy for 300 g shaft, would be enough to neil some medium size fish. In your case with 570 g shaft it would be 25 J. Is it enough for your target pray (DOG).? I don't know.. You can maybe find out yourself. If you put your Miraqe Evo on 2 bar or maybe somewhat more (2.4) because of the friction of the piston. you would have initial speed of about 10 m/s. Try to shoot some target (body or head of a big fish) from 2 m distance out of the water, in air. You will see is if it enough to neil through the fish. If it is not, increase the pressure and try again. Then calculate the speed and the energy of the shaft with that pressure. You will have the data for your max shooting distance.
Another way to test what could you expect from a spear at speed 10 m/s, without even shooting it from the speargun is to let the spear fall down to some target from a high 5,1 m. It is from formula for free fall h = 10 *10/(2 * 9.81)= 5.09 m
 
Bad news for Diving Gecko (Davide) end his Mirage Evo, as could be calculated from diagram above or excel file, is that even for initial speed v0 = 44 m/s (that is 33 bar/loading effort 45 kgf) using 2 mm Dyneema, speed on 5 m would be only about 10 m/s. I actually got 9,6 m/s with 483 g spear. His spear is 570 g so it would be somewhat more. On 4 m about 14 m/s. If using 1,5 mm mono speed on 5 m would be about 20 m/s.
This is just en estimation but might be very close to real situation...
Because I made a correction to function y=e(-0,38x) to be y=e(-0,3x), speed at 5 m would be instead of 10 m/s higher: 13 m/s,
But because this calculation had been done using very rough rope of 2 mm (there is an image if it in #11) I did a new calculations for mono 1.4 mm and mono 1,7 mm. (Mono has less drag in water than Spectra/Dyneema so results are better than with Spectra)
For same initial speed v0 = 44 m/s speed of the shaft at 5 m would be 13.2 m/s for the shaft 483 g.
-for 1.4 mm mono - 20.4 m/s
-for 1.7 mm mono - 17.3 m/s
-for 2 mm rope - 13.2 m/s
I can not say what would be the expected results with heavier shaft (570 g) because I did not made measurement with such shaft or at least three different weight shaft... I only know that results (speeds) would be better then here calculated.
Some of you did not catch the point... These results have nothing with the design or brand of particular speargun or friction of the piston, as long it is able to achieve the desired initial speed of the spear.

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I personally did not put any thought into whether your formula was brand dependent or not (though I have some thoughts on it now; more on that later). But as I said, I don't have a need for the math now as I don't have any idea if 13m/sec is enough or not enough for my target prey. Nor do I know what speeds my friend's bandguns shoot at so I can't compare to them either though I know they have sufficient power for what we hunt. As such, any speed or energy values are a curiosity at this stage.

That said, I think it's good having this thread as others will have some better references. And with time, I will find use for it, too and can hopefully share my own, real speed findings from the pool compared with penetration tests.
To get back to whether your numbers are brand dependent or not, how did you come up with the initial speed for my shaft at a certain gun pressure, if you did not assume that the efficiency of the design was the same as your "base gun"? I am curious, I am not criticizing and I am beginning to wonder how different the different guns really are... Perhaps not very different.

If we do want to entertain the idea of getting more real data, some years ago Omer were very proud of their test pool and its impact sensor. It really shouldn't be that hard making something like that these years as electronical sensors have come down in price a lot. If someone has a good grasp on Arduinos and sensors perhaps they can come up with something? I wouldn't mind making one, but I am not right guy to design it at all.
 
The speargun tests for muzzle velocity that I referred to were done with a Chronoscope which is a device normally used for air rifles. The water testing required it to be waterproofed and it functions by measuring the transit time over a short distance out from the muzzle and that then determines the velocity. For the speargun tests the Chronosope has to be placed where the gun ceases pushing on the spear, hence ideally it should be placed one spear length from the muzzle. If you place it directly in front of the muzzle then the emerging spear head will trigger it, but the piston will still be pushing the spear and therefore the spear has yet to reach maximum velocity.

https://www.airgunshooting.co.uk/airgun-guru-should-every-airgun-owner-have-a-chronoscope-1-4744579
 
Pete, thanks for the link!
But just to remember you, I've developed, built and used several types of device (total four) dedicated to underwater measuring speed of the shaft.
I've measured speed of the shaft on different distances including at distance one spear length from the muzzle - the initial speed of the shaft.
https://forums.deeperblue.com/threads/measuring-speed-of-the-shaft.91007/
Davide, initial speed of the shaft can be obtained on more different ways: by measurement or by calculation.
In your case I proposed calculation because it was the most convenient method. If the speargun is well built and in good condition it is quite adequate method. You just have to know few input parameters:
1. working stroke of the piston
2. weight of the shaft
3. Air pressure in a speargun.
4. CR - compression ratio
I just measured the CR for my Cyrano 850 yesterday. (Loading force just before cocking) / (loading force at the beginning of pushing the piston)
I've got for CR=1.2
For initial speed calculation other factors as type and thickness of the line, the slider used ar not important.
It is even not very important that you know the exact initial speed of your speargun, at least for beginning.
It is useful to know what could you expect from some configuration (shaft, line combination) and to see if it is worth to increase the pressure in speargun above some point.
You can see If some improvement in performance (energy of the shaft on target distance - 5 m or 6 m) is worth increasing the pressure (loading effort)..
Of course it would be useful if you know what speed/energy of the shaft is sufficient on target distance for specific fish hunt.
 
This was an interesting fact what I discovered regarding measured and calculated initial speed in my post:https://forums.deeperblue.com/threads/measuring-speed-of-the-shaft.91007/#post-850825 from Jun 18, 2011.
At that time I wrote:

"It was more difficult to measure the speed of the shaft than I thought it would be. This is the last setup with a sewing thread, and it works. I was using Tomba10 vacuum barrel, 1.5 mm mono and slider as on the picture. Distance to calculate the speed from measured time was 0.172 m.
Per calculation a got that the speed of the shaft should be 31.7 m/s. This speed might be even higher if the drag of piston is less than 1.2 kg. I measured the total drag of piston, shaft to cone ring during loading and unloading the gun. If the piston drag would be 0.8 kg instead of 1.2 kg than the speed in air would be near 32 m/s.
What I got as a result of measurement was:
0.2 m after the shaft separate from the piston the speed was 33.1 m/s
(3.4 % more than 32 m/s)."

So I got per calculation the speed to be 31,7 m/s, but later (maybe a month later) I discovered that may kitchen scale was faulty! I measured the weight of the shaft to be 334 g but it was actually 301 g. CR = 1.2. Friction of the piston is about 1.2 kgf.
Length of piston acceleration path for Cyrano 850 is 0.670 m. Pressure was 25 bar.
With new input data I've got for calculated initial speed to be 33.3 m/s what is very close to measured speed of 33.1 m/s.
 
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I just found an image of measurement with Cyrano 1100 with 7 mm free shaft at 32 bar using 1.5 mm mono.
Excel file for calculation is attached too. Initial speed was 42 m/s. I'm not 100 % sure about the exact length and weight of the shaft used but it was in original box with the speargun... I've sold it few years ago so I can not check it but it might be about 1250 mm and 376 g?


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