How can one know where to throw one's spear when spearfishing?
Spearfishing has been around ages and everyone has heard of how great the Native Indians were at spearfishing.
As we all know, light is refracted (bent) when it enters water. The key to spearing fish is to know how much below the fish to aim the spear from the edge of a river or stream.
What is the science principle of understanding where to throw a spear into the water in order to catch your fish?
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This is a great explanation of the concept:
Investigating refraction and spearfishing
Refer to the linked Word document inside. It is copyrighted, so I hesitate to include its contents in entirety here.
No matter the angle, no matter the position, you always aim for below the apparent position of the fish.
The apparent position of the fish actually becomes closer to the surface for when further away from the fish. When a person is viewing from a position more directly above the fish, its apparent position is three-quarters of the actual depth of the water. To estimate the actual depth of the fish, estimate how deep it appears to be and add and extra one-third of this distance.
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The math is trigonometry but I think you would need to get a feel. It is not like you could run the math on the fly anyway.
The ratio of sin above and the sin below is 1.33.
More angle is more bend. At perpendicular there is zero bend. At 45 about 13 degree of bend.
At 45 degrees if the fish looked like a depth of 2' you would need to aim like 7" below by my calculation. You still have to guess how deep the fish looks. Multiply how deep it looks by 1.33.
The best thing would be to set up a string and a target and practice. The spear is also going to push off when it enters the water so need to account for that.
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The easy technique is to simply hold the spear in your hand with the tip under the water and stab the fish. Once your spear enters the water, refraction has identical effects on your view of the spear point and your view of the fish, so you can easily guide it to where you want.
Throwing a spear to hit a fish takes a great deal of practice. The physics of refraction is sufficiently non-linear that the only practical way is trial and lots of error.
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