Mar 2013
4:50pm, 30 Mar 2013
15,650 posts
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FenlandRunner
Depends? Thinking of the trajectory? Difficult to explain in text, but should the goal should be glide, shallow trajectory?
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Mar 2013
5:52pm, 30 Mar 2013
18,183 posts
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SPR
The time is still governed by how far up you go, the glide forward is all about how fast you are going but does not have an effect on how long it takes to come back to the ground. Gravity is the only thing that brings you down and forward speed does not counteract gravity.
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Mar 2013
5:53pm, 30 Mar 2013
549 posts
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Canute
FR The shape of the trajectory during airborne time is fixed by gravity (if we ignore wind) as gravity s the only external force acting on the body during flight For half the airborne time, you are going up and for the other half you are coming down. The COM must follow a parabolic arch during flight (ignoring the effect of wind resistance). If airborne time is T sec, you are falling at 32 ft/sec/sec (or 9.8 m/sec/sec) for T/2 sec. Thus if the airborne time is 0.25 sec, the body must rise and fall by 7.66 cm during flight (I am using cm to avoid making Glenn snigger). If you are travelling at 3.33 m/sec (ie 5min/Km or 8min/mile) the base of the arch is 83cm.
However, the total vertical motion of the COM is further increased due to the fact that the COM continues to descend during the first part of stance. The amount of descent of the COM while on stance depends on the tension in the leg muscles, so you have some control over this. However, the motion of the COM whilst on stance is only a minor part of the overall trajectory. So the shape of the major part of the trajectory on the COM is fixed by gravity, airborne time and pace.
If you want to minimise the distance of vertical travel during airborne time, you can do this by one of only two things: 1) spend longer on the stance, thereby increasing braking costs; 2) increase cadence. At medium and fast speeds, increased cadence is usually the best option, though there is a limit to the optimum cadence because limb repositioning cost increases with cadence. At very low speeds, it is OK to spend a little longer on stance because braking costs are relatively low, due to the lack of obliquity of the leg, as explained in my previous posting.
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Mar 2013
6:46pm, 30 Mar 2013
15,654 posts
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FenlandRunner
I've no idea about mechanics, but does angle of force not matter?
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Mar 2013
9:55pm, 30 Mar 2013
550 posts
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Canute
FR, As described above, while the body is airborne, the COM must follow a parabolic arch, the same as a projectile such as a cannonball. You raise a reasonable question about whether the angle of force (and angle of motion) at take-off will shape the trajectory. Yes it does, but this does not give you the freedom to adjust stride length and vertical range of motion independently. Once you have selected the range you wish to achieve with a cannonball, the angle of take-off is fixed, and similarly, once the runner has selcted speed and airborne time, the angle of take-off is fixed.
The angle of take-off determined by the ratio of the vertical velocity at lift off to the horizontal velocity at lift off. In the example we are considering, the horizontal velocity is 3.33 m/sec (= 8 min/mile). We also assume we were aiming for an airborne time of 0.25 sec. This will allow us to travel 3.33 * 0.25 metres (= 83 cm) while airborne.
If we are to achieve an airborne time of 0.25 sec, we must exert just the right amount of vertical force to keep the body moving upwards against gravity for half of 0.25 sec. During the first half of the 0.25 sec period (ie 0.125 sec), the body is decelerated at the rate of 32 ft/sec/sec (9.8 m/sec/sec), and reaches zero upward velocity at the end of this period. The distance travelled when a body is being decelerated by gravity to achieve zero upward speed after 0.125 sec is the same as the distance that a body will fall under the influence of gravity in the same period. As discussed in my previous post, this is 7.66cm.
If you exerted a weaker upwards push , you would remain airborne for less than 0.25 sec and your stride length would be shorter. So you cannot avoid lifting the body by 7.66 cm if you want to a horizontal distance cover 83cm while airborne at a pace of 3.33 metres/sec.
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Mar 2013
10:04pm, 30 Mar 2013
551 posts
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Canute
Sorry for the slightly garbled grammar. The final sentence should be:
So you cannot avoid lifting the body by 7.66 cm if you want to cover a horizontal distance of 83cm while airborne at a pace of 3.33 metres/sec.
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Mar 2013
11:24pm, 30 Mar 2013
7,023 posts
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GlennR
Brilliant stuff Canute. Exactly what I was trying to grope for with my original question but far in excess of anything I could managed.
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Mar 2013
9:57am, 31 Mar 2013
15,655 posts
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FenlandRunner
'while airborne' is crucial in that sentence as it isn't the same as stride length.
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Mar 2013
12:23pm, 31 Mar 2013
1,169 posts
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shanksi
Very interesting posts, Canute. Your comments about running at slower speeds really chimed with what I've been thinking (although I am by no means an expert nor have I studied it in great detail - I just have a wee bit of personal experience of running slowly )
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Mar 2013
1:09pm, 31 Mar 2013
552 posts
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Canute
FR It is true that distance covered while airborne is not the same as stride length. I was trying to avoid making things too complicated by focussing on airborne time in that comment.
If you follow a shallow trajectory and cover less distance while airborne, you will in fact spend longer on the ground, and make up some of the stride length as your COM moves over your stance foot. However, as mentioned in an earlier commet, you will incur greater braking cost. So, as discussed earlier in this discussion, there is a trade off between the cost of elevation and braking cost. At very low speed, the braking cost is not too severe because of the lack of obliquity of the leg, but at medium and high speeds, you are better off spending more time in the air.
While we should not base too much on one exceptional runner, I think that picture of Paula Radcliffe at mile 14 on her way to victory in the NY marathon is an interesting illustration that backs up what the principles of biomechanics tell us.
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