In the movies, arrows shot into the air rotate so that during the descent, the arrow head hits ground first. What is the source of this angular momentum? It would seem that the bow string exerts a force directly in line with the arrow.
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4$\begingroup$ Gravity? I believe this question severely needs to be accompanied by a film clip or illustration for it to be clear $\endgroup$– SteevenCommented Jun 22, 2016 at 21:46
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3$\begingroup$ @Steeven: no, not gravity, see the answers. If you fired an arrow above the horizontal in a vacuum then (supposing it didn't manage some large fraction of a complete orbit) it would land tail down. $\endgroup$– Steve JessopCommented Jun 23, 2016 at 9:01
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18$\begingroup$ @WaqarAhmad Why is this question "pervert"? $\endgroup$– OddDevCommented Jun 23, 2016 at 9:43
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6$\begingroup$ Consider the same answer with a shuttlecock ("badminton ball") if you have practiced badminton more than archery. I think we need to put people on the Moon again and have them shoot arrows and play badminton to see how things work out with no air. $\endgroup$– Jeppe Stig NielsenCommented Jun 23, 2016 at 15:05
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3$\begingroup$ It's not just in the movies; in real life, arrow heads weigh more than feathers, too. $\endgroup$– TylerHCommented Jun 24, 2016 at 2:00
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7 Answers
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The same reason objects which are heavier on one side tend to fall with the heavy side down: the tip of the arrow is denser than the rest of the arrow. The center of gravity is offset from its geometrical center, so the air drag, which is based on the object's geometry, causes a torque together with gravity as seen in this very professional picture of a body falling straight down.
answered Jun 22, 2016 at 22:03
AccidentalTaylorExpansionAccidentalTaylorExpansion
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35$\begingroup$ This is only part of the explanation, and probably a small part. The fletching are the key. There is a reason you don't see arrows/quarrels/darts without them. $\endgroup$ Commented Jun 22, 2016 at 22:36
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17$\begingroup$ @dmckee all that the fletching does is move the point on which Fdrag pulls on the arrow. $\endgroup$ Commented Jun 23, 2016 at 6:01
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28$\begingroup$ The fletching is not the key. Arrows without any feathers have exactly the same behaviour. Fletching is only needed to correct technical failures of the archer (sloppy release etc.). Check out bareshafts and you'll see that they fly exactly the same if correctly shot. There are even a few tribal people who shoot without any feathers. The key here is the F.O.C. which has to be between 10 % and 15 % to make an arrow fly. $\endgroup$– OddDevCommented Jun 23, 2016 at 7:44
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11$\begingroup$ @dmckee, heavy tip alone works (compare javelin), fletching alone works too (some arrows did not have heavy tips), if used together, the effect combines. Either way, the reason is that centre of drag is behind centre of gravity. Heavy tip moves centre of gravity forward, fletching moves centre of drag aft. $\endgroup$ Commented Jun 23, 2016 at 15:23
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6$\begingroup$ @MasonWheeler, yes, if you shot an arrow in vacuum, it would not orient itself point forward. It would probably rotate, because you likely won't manage to shoot it without any angular momentum—just not in relation to where it flies. $\endgroup$ Commented Jun 23, 2016 at 15:27
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Air.
Conservation of angular momentum does infact dictate that whatever rotation it starts with it should end with, provided nothing else acts on it. Air allows its forward momentum to act on it.
Consider a weather vane, a wind sock, or a flag. They rotate when not facing into the wind because one side presents more wind resistance than the other. Once wind resistance is minimized by facing into the wind, they stabilize.
Consider a cannon ball on a windless day. Like any ballistic object it travels in a parabola (or nearly one, considering air resistance). Throughout its trajectory, doesn't the direction of the air flow it experiences change in line with its trajectory?
This graph could be seen as both the path of a projectile and as a vector field for the air flow (or relative wind) force experienced by that projectile at different points along its journey.
Consider TPing someone's house (just not mine please). If you unroll some of the toilet paper from the roll before throwing it doesn't the paper show the direction the wind is passing (relative to) the roll?
Consider an arrow. Why should it be any different?
Ah, but consider a stick. Toss a stick and it doesn't rotate into the wind. Why not? Because the wind resistance is the same on both sides. So neither one wins.
It's about where the center of mass is (thus where it rotates) and which side of that center offers more wind resistance.
As for arrows, the mass of the head puts the center near the front, away from the fletching (feathers). The head offers little wind resistance.
The fletching offers a lot when not in line. Since the fletching is far from the center of mass, it also has good old fashioned leverage.
Even without the fletching the shaft offers wind resistance. More shaft on one side of the center of mass means more wind resistance on that side. The end with more wind resistance on it's side of the center becomes the tail of the arrow.
If you don't believe me, balance an arrow on your finger and blow on it. You just made a weather vane.
You might some day shoot arrows on the airless moon. I don't think you'll find them reliably landing headfirst.
answered Jun 23, 2016 at 4:26
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3$\begingroup$ This is the same as user3502079's answer but is much more clearly explained. Good job $\endgroup$ Commented Jun 23, 2016 at 7:31
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3$\begingroup$ What does "TPing" mean? Toilet-papering? That is, throwing toilet paper at it? $\endgroup$ Commented Jun 23, 2016 at 10:06
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5$\begingroup$ Wow, just looked it up. TPing means throwing a roll of toilet paper so it unrolls in the air. I suspect many people (like me) have absolutely no experience in doing this, so you might want to find a more intuitive example. $\endgroup$ Commented Jun 23, 2016 at 10:11
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3$\begingroup$ If there is air resistance, the trajectory is not a parabola. So it is weird to talk about a parabolic trajectory showing the vector field of air drag. (I didn't downvote FWIW). $\endgroup$ Commented Jun 23, 2016 at 12:26
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2$\begingroup$ @MikeDunlavey thanks! It clearly shows how under appreciated toilet paper is as a physics toy. $\endgroup$ Commented Jun 25, 2016 at 17:58
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In the movies, arrows shot into the air rotate so that during the descent, the arrow head hits ground first. What is the source of this angular momentum?
An arrow shot on the Moon would not do that. Air and the geometry of the arrow are key. An arrow flying through the air is subject to two forces, gravity and aerodynamic drag. Gravitation will not make an arrow turn during the course of its flight. Gravitation results in a curved trajectory by the center of mass, but it does not make an arrow turn. Aerodynamic drag makes a properly-designed arrow or rocket follow a zero (or near zero) angle of attack trajectory. The angle of attack of a flying object is the angle between the object's velocity vector with respect to the air and a reference line on the object. In the case of an arrow, that reference line is along the shaft of the arrow.
The key feature that makes an arrow or rocket stable with regard to deviations from the desired flight angle is to have the center of pressure, the point at which the drag forces effectively act, be behind the center of mass. Suppose an arrow is flying at some small but non-zero angle of attack. This will make the drag force have a component that is normal to the shaft of the arrow, resulting in a torque on the arrow. If the center of pressure is ahead of the center of mass, this torque will make the arrow turn even further away from a zero angle of attack. This is unstable; such an arrow (or rocket) would try to flip around. With the center of pressure behind the center of mass, this torque will make the arrow turn toward a zero angle of attack. Having the center of pressure behind the center of mass results in a restoring torque that makes the arrow flies true.
An arrow has a somewhat heavy arrowhead at the tip that typically places the center of gravity in front of the geometric center of the arrow. Archers sometimes add weights inside the arrow's shaft to move the center of mass. The head itself offers some drag, but most of the drag comes from the arrow shaft itself. This naturally places the center of pressure behind the center of mass, even for an unfletched arrows.
Fletching makes an arrow behave better, but it is not essential. Adding fletching moves the center of pressure considerably more rearwards than the center of mass. This is one of the reasons fletched arrows are more stable than are unfletched arrows (also called bare shafts). Another thing that fletching does is to makes the arrow spin about the shaft axis, adding gyroscopic stability.
answered Jun 23, 2016 at 15:05
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1$\begingroup$ This meets with my expectations. Even if fletching is not the key, it must be at least useful. High axial angular momentum and increased air drag in perpendicular directions are, at least in my view, associated to fletching. Even if you remove the fletch and rely entirely on weight balance, something must be lost. $\endgroup$ Commented Jun 23, 2016 at 15:25
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As pointed out by dmckee in his comment, anyone (including myself) that has practised bow and arrow knows the arrow by weight and fletch inspection. As my English corrector points out, fletch doesn't seem to be a very commom word: it means that feather at the end of the dart/arrow. Everything resumes to how good is the fletching.
When shot the arrow wants, as any other object, to spin around its centre of mass. It doesn't matter if the centre of mass is closer to the tip or to the end of the arrow, the fletch will increase air drag in directions perpendicular to the arrow's instant velocity, making it harder to spin around the centre of mass. If the tip is heavier than the end, the arrow starts descending tip-first, but it's the fletch that sustains that direction of flight; if the tip is not heavier and the weight is balanced, the arrow still flies pretty well; if the weight is to the end of the arrow, it simply goes crazy. Now, another function of the fletch is to make the arrow spin along its axis (this increases stability even more, since the arrow acquires axial angular momentum) , and to accomplish this the fletch slightly spirals towards the end of the spine.
Something that must also be pointed out is that weight distribution, material resistance and flething are also calculated to predict the effect caused by the Archer's paradox. Balance between tip weight and fletching are fundamental, but modern bows have a design that virtually kills the flexing of the arrow (centre-shot bows).
answered Jun 22, 2016 at 23:38
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6$\begingroup$ Nope, bareshafts (arrows without feathers) forums.bowsite.com/tf/pics/00small54200834.JPG do exactly the same. $\endgroup$– OddDevCommented Jun 23, 2016 at 6:46
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1$\begingroup$ I must admit I'm completely baffled by the bare existence of bareshafts. I practised archery with English longbows and the fletching was an absolute must. I would swear arrows without fletching didn't exist... But then I think about a good spear and I must admit that even though they don't have feathers they fly straight. The only thing I insist on is that the fletching is fundamental to help the arrow acquire angular momentum. $\endgroup$ Commented Jun 23, 2016 at 14:41
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1$\begingroup$ I wouldn't insist too hard on that ;P A bareshaft rotates: tap46home.plus.com/mechanics/fbare.htm "In practice the (bareshaft) will rotate under the net effect of the drag and vortex shedding torques." $\endgroup$– OddDevCommented Jun 23, 2016 at 14:54
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2$\begingroup$ @OddDev - QuantumBrick was (I think) writing about the hundred to over a thousand RPM roll rate of a fletched arrow rather than the orders of magnitude smaller pitch rate of an arrow makes while flying at zero angle of attack. $\endgroup$ Commented Jun 23, 2016 at 15:14
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$\begingroup$ I totally was. Sorry for being obscure. $\endgroup$ Commented Jun 23, 2016 at 15:19
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The arrow ideally will fly out like a drag race car with the parachute deployed!
A well designed arrow should have these properties.
1- Sharp and proportionally heavy point to accept a large momentum and deliver it as kinetic energy E= mv^2/2
2- long and balanced stem to accommodate a big arch and maintain separation between the tip and the fletching.
3- an aerodynamically well designed fletching to keep the arrow straight and also provide the small amount of drag needed to keep the end of arrow always steady behind the tip and prevent the stem from getting disoriented.
The reason the arrow fly aligned in its arc is the small drag created by fletching always position it aligned with its track, same as badminton ball.
In aerodynamic design this scheme of installing the rudder and elevators at the end of fuselage for stability is common practice! All airplanes have it as empennage or tail end!
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To follow up from the excellent answers of @AccidentalTaylorExpansion and others, I've constructed a diagram showing the weather vane effect of the drag force vector acting on a diagonally shot arrow or javelin at t = 0 and t = 0 + delta t. The two forces acting on the arrow are gravity and air drag. The effect of gravity on the velocity of the center of mass is to move the c.o.m. in a parabolic trajectory. The drag force always opposes the motion of the arrow, and acts on the geometric center of the arrow, at a distance r from the c.o.m.
Because the orientation of the c.o.m. velocity vector changes (rotating clockwise in my diagram), the direction of the drag force on the arrow also changes (also rotating clockwise). This leads to a weather-vane effect on the arrow/javelin, creating a negative torque about the center of mass (directed into page) and a clockwise instantaneous acceleration.
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The fletching is the most important aspect. Load a dart into a catapult in such a way that the pointed end is pointing at the ground. Immediately after firing it, the dart aligns itself with the direction of flight and in this case the 'heavy' end is rotated upward proving that the weight distribution is not the cause of the rotation, because it is rotating the opposite way to what the weight distribution predicts.
Now load the dart so that is it rotated 90 degrees horizontally from the intended flight direction. On release from the catapult, the dart will rotate horizontally to align itself with the direction of flight and this can not be explained by gravity, because that force acts vertically.
An arrow fired high into the air follows the typical curved trajectory of any projectile and the orientation of the arrow is always tangential to the curve thanks to the drag of the fletch. On the way back down the trajectory is pointing downwards so the arrow also points downwards.
The situation would of course be different in a vacuum, but that is not the normal situation.
