Question

I need help with solving for dimensionless speed, and actual speed for a dinosaur.

thanks

Dinosaur	Foot Length (m)	Stride Length (m)	Leg Length (m)	Relative Stride Length (RSL)	Dimensionless Speed (DS)	Actual Speed (m/s)	Actual Speed (mph)
Hadrosaur	0.3	1.4	1.2	1.17	0.15
Velociraptor	0.25	2.72	1	2.72
Stegosaurus	0.35	1.90	1.4	1.36

1. All juvenile tetrapods tend to have relatively larger feet (i.e. puppies). Assuming the tracks you worked with were those of young dinosaurs, how would your results be affected?
2. Could you outrun a velociraptor dinosaur? Justify your answer with the measurements you worked out. Keep in mind that most of the times animals proceed at walking speed

Answer 1

From the data given in the table, we can calculate the Dimensional Speed(DS), Actual Speed(S) by using following formulas:

1. Dimensional Speed(DS):

where, RSL is Relative Stride Length

2. Actual Speed (in m/s):

  

where g = acceleration due to gravity (9.8 m/s2)

3. Actual Speed ( in mph):

To convert a meter per second measurement to a mile per hour(mph) measurement, multiply the speed by the conversion ratio. One meter per second(mps) is equal to 2.236936 miles per hour, so use this simple formula to convert:

So by using all above formulas, we can get required values as:

Dinosaur	Foot Length (m)	Stride Length (m)	Leg Length (m)	Relative Stride Length (RSL)	Dimensionless Speed (DS)	Actual Speed (m/s)	Actual Speed (mph)
Hadrosaur	0.3	1.4	1.2	1.17	0.15	0.51	1.14
Velociraptor	0.25	2.72	1	2.72	1.56	4.88	10.91
Stegosaurus	0.35	1.90	1.4	1.36	0.32	1.18	2.64

1] From the resut obtained, we can say that,

Relative stride legth depends on the leg length by the relation

that Relative Stride Length is equal to the stride length divided by the leg length.

So that Relative Stride Length is inversely proportional with Leg length. Therefore, as Leg length increases, Relative Stride legth decreases. Since Dimensional Speed(DS) depends on Relative Stride length, Dimensional speed and Actual speed also affected.

Therefore, if we assume that the tracks we worked before were those of younger Dinosaur then their size of leg (leg length) must be different than the actual one. Hence, this result should be change for other tracks of respective Dinosaur.

2] According to the result obtained for Velociraptor, we can say that,

Its actual speed also depends on the leg length. Its actual speed is more than the other two species mentioned here. Actual speed of Velociraptor is about 10.91 mph.

On the other hand, under normal conditions, grown normal people should run at 15 mph, while sprinting at 20mph (32km\h). This is more than the actual speed of Velociraptor. Since the most of the times animals proceed at walking speed, so we can easily outrun Velociraptor by running with speed more than a 12 mph.