Where is the most amount of strain in both situations? What are the health disadvantages for both?
What will be the effects when increasing to a sprint?
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Ankle weights will affect how your legs move as you run, and will likely cause injury. Weighted belts won't change your biomechanics much, but a greater impact can lead to injury as well. Even if you accelerate to a sprint, weighted ankles will keep your legs from moving normally. The weighted belt, on the other hand, won't affect you much at all in a sprint.
If you're interested in getting faster (both for distance events or sprinting), I would recommend other training methods.
Ankle weights will affect how you move your legs and put additional strain on your knees, which isn't a great idea. (i.e: it's a terrible idea)
Weighted belt is a better way to add weight, but will be rather uncomfortable. A weighted jacket provides better weight distribution.
However, I would challenge the reason why you want to add weight while running.
Running puts already quite a lot of stress on your joints, and increasing the weight just means increasing the potential for injury. Not worth it.
You need to think about what you are trying to achieve, and look into the solid proven training methods to achieve those goals.
For instance, if you want to burn more, just pick up the pace or do intervals - you will burn more, guaranteed.
if you want to improve your sprint times, loading up on weight while running is NOT the solution. A much better idea would be a weight training program with squats, deadlifts, cleans with heavy weights combined with uphill sprints and interval training - and of course regular sprints.
To increase strength significantly, you need heavy loads, and as heavy loads are dangerous, you need to handle them with safe controlled movements like squats and deadlifts, not running around and getting tired with carrying heavy loads. Besides, if you can do more than 10 reps, it's not heavy enough, so forget about running with weight, just do your squats, deadlifts and cleans.
If you insist on running with weights, a good solution is sled work. Go for about 10% body-weight for sprints and you will gain speed.
What you should NOT do is anything that puts your joints at risk. Injure a knee and you will be out for 6 months. Totally counter productive.
Your first step is to clear up your goals, what you want to achieve, and research a program to do that.
Both can increase the risk of injury. The belt will put pressure on knees and the weighted ankle will put pressure on hips.
It can be done without injuries if controlled carefully. Both can help developing force, but because of the risks, other methods are preferred.
Running with extra weight leads to muscle mass increase. The benefits could be higher in endurance running, if the weights are decent.
I ran with heavy military boots in one winter and the core strength developed great, but it didn't improved the speed.