Post by Theropod on May 1, 2014 20:38:33 GMT
Misconceptions to do with scaling are very common. It's important to know what the square cube law has to do with scaling. If an ant weighing 1 milligram lifts 50 milligrams, most people will believe an ant weighing 1kg will lift 50kg. No, it will not. If an animal were isometrically scaled up by a considerable amount, its relative muscular strength would be severely reduced, since the cross section of its muscles would increase by the square of the scaling factor while its mass would increase by the cube of the scaling factor.
In the case of flying animals, the wing loading would be increased if they were isometrically scaled up, and they would therefore have to fly faster to gain the same amount of lift. Air resistance per unit mass is also higher for smaller animals, which is why a small animal like an ant cannot be seriously injured from impact with the ground after being dropped from any height.
As was elucidated by J. B. S. Haldane, large animals do not look like small animals: an elephant cannot be mistaken for a mouse scaled up in size. This is due to allometric scaling: the bones of an elephant are necessarily proportionately much larger than the bones of a mouse, because they must carry proportionately higher weight.
If a man is 1.80m tall, weighs 80kg and lifts 100kg, he lifts something 20% heavier than himself. But if we make him 2 times taller (3.6m), he will weigh 8 times more:
80*(3.6/1.8)³ = 640
Since we are scaling mass, his mass will increase by the cube of the scaling factor. Strength increases by the square of the scaling factor, so this is how we calculate how much he will lift at 3.6m tall and 640kg:
100*(360/180)² = 400
Now he can lift 400kg, 62.5% of his total weight, which means he is now 50% weaker proportionally. Examples of this really happening with people include weight lifting. The record holder in the lightest category (56kg) is 1.52m tall and weighed 56kg, his record is 168 kg, he is able to lift exactly 3 times his own weight, let's see the heavier categories. In the 77kg category, the record holder is 1.7m tall and weighed 76kg, he lifted 207kg, only 2.7 times his own weight. In the 94kg category, the record holder is 1.74m tall and weighed 94kg, he lifted 233kg, only 2.5 times his own weight. In the +105kg category, the record holder is 1.86m tall and weighed 163kg, he lifted 264kg, only 1.6 times his weight. Of course, he was also a bit fat, if he had the same body fat percentage as the previous ones he would be stronger in relation to his own weight, but the point is that as you get taller and bigger you lift proportionally less than someone smaller.
This thread is just to get the main point across, use it to discuss scaling topics.
In the case of flying animals, the wing loading would be increased if they were isometrically scaled up, and they would therefore have to fly faster to gain the same amount of lift. Air resistance per unit mass is also higher for smaller animals, which is why a small animal like an ant cannot be seriously injured from impact with the ground after being dropped from any height.
As was elucidated by J. B. S. Haldane, large animals do not look like small animals: an elephant cannot be mistaken for a mouse scaled up in size. This is due to allometric scaling: the bones of an elephant are necessarily proportionately much larger than the bones of a mouse, because they must carry proportionately higher weight.
If a man is 1.80m tall, weighs 80kg and lifts 100kg, he lifts something 20% heavier than himself. But if we make him 2 times taller (3.6m), he will weigh 8 times more:
80*(3.6/1.8)³ = 640
Since we are scaling mass, his mass will increase by the cube of the scaling factor. Strength increases by the square of the scaling factor, so this is how we calculate how much he will lift at 3.6m tall and 640kg:
100*(360/180)² = 400
Now he can lift 400kg, 62.5% of his total weight, which means he is now 50% weaker proportionally. Examples of this really happening with people include weight lifting. The record holder in the lightest category (56kg) is 1.52m tall and weighed 56kg, his record is 168 kg, he is able to lift exactly 3 times his own weight, let's see the heavier categories. In the 77kg category, the record holder is 1.7m tall and weighed 76kg, he lifted 207kg, only 2.7 times his own weight. In the 94kg category, the record holder is 1.74m tall and weighed 94kg, he lifted 233kg, only 2.5 times his own weight. In the +105kg category, the record holder is 1.86m tall and weighed 163kg, he lifted 264kg, only 1.6 times his weight. Of course, he was also a bit fat, if he had the same body fat percentage as the previous ones he would be stronger in relation to his own weight, but the point is that as you get taller and bigger you lift proportionally less than someone smaller.
This thread is just to get the main point across, use it to discuss scaling topics.
