Every Dog Team Must Jump The Same, George

Early in the movie, Spirit of the Wind, George Attla Sr. points out two dogs in the trapline team and comments in those same words to young George.
What does it mean?  Multiple choice test, check it out!
A. All sled dogs in all dog teams must have the same frequency or rpms when running
B. All the dogs in a given team must be trotting or loping or pacing but not mixed in the same team
C. All the dogs in a particular team must be jumping the same distance which means they must be jumping at the same frequency
D. All the dogs in a team are jumping or kicking simultaneously like the chorus line in a Broadway musical
In a book about human running and training for racing, Jack Daniels describes his eye-opening experiment during an Olympic Games. He and his wife timed the runners’ footfall frequency for various running events. They found that the best performers had the higher rpms, about 90 or more. (In bicycle racing high RPM is also associated with best performance.) In the book, Jack Daniel’s Running Formula he develops other useful models for predicting race results based on heart rate, times over trial distances and other indices or proxies for success in running. For world class human runners this corresponds partially to answer A above.
Dogs’ leg frequency when running free and when pulling are not necessarily the same for an individual dog and certainly not identical for all dogs.  Each dog is bouncing against or on the tugline. If you drag something or pull against a load on wheels, you lean into the line and start walking but you have to time or coordinate your steps and the angle you are leaning with the bounce of the pulling line. So you can appreciate the importance of these same factors to a sled dog.
It is evident that the harness and gangline affect a sled dog’s gait when you let a dog run free on a packed snow surface or bare ground after that dog has been pulling a sled. This is especially noticeable for dogs that are loping and not so important for trotting. The dog does not extend as far forward as would normally running free or in the team, as if running on slippery ice. The free running dog takes time to adjust to the change, the absent tugline and sled to pull against. In the team the dog relies on the harness and gangline to pull against, stopping the forward momentum at the moment the front feet are hitting the ground. And that is the moment when the most energy is transferred to pull the sled, to some degree this is energy that would be lost to ground reaction forces otherwise.
How can the system transmitting the pulling forces generated by the dog to the load be most efficiently and effectively coupled with the dog’s body resonant frequency?
The appropriate/corresponding body oscillation/resonant frequency for a dog trotting vs. loping may be approximately doubled for trotting. (Although this may not be significant in harness and gangline design)
The simplest practical way to address the problem of coupling is to use a cable gangline to isolate the dogs from each other. The elasticity in a poly plastic hollow braid centerline is probably too great to be efficient at the dogs’ resonant frequency and actual mechanics of pulling, but the resonance of the lines bouncing up and down are also in play…
Static deflection d is the distance an isolator or coupling spring will deflect under the static or dead weight of the equipment
d=g/(2*pi*f)^2     using spreadsheet operator symbols
This formula gives the resonant frequency  f as a function of static deflection under the mass/load. (Inertial and gravitational mass are the same so they drop out of the equation.)

A dog loping leg frequency was eyeballed in the range of 2.5/sec

Solving for d:

Damn if  I can remember what the units are…

When I did this before I calculated that d was about 1.5 inches/4 cm. That means that to tune the gangline and harness to the dog’s frequency you should be able to hang the weight of the dog on the optimum coupling spring with the same elasticity/spring as the dog experiences going back to/coupling to the cart or sled and the weight will deflect 1.5 inches.

g is the gravitational acceleration, 9.81 m/sec^2, so  f = 2.5/sec returns d = approximately .04 meters, 4 cm

In my interpretation that means the optimum spring/elasticity is quite stiff in relation to the the actual pulling forces of dogs running in harness. If the dog’s actual pulling force is 1/10th it’s M x g, we could say weight, (but probably exerted only over a fraction of the cycle) the system will only deflect .15 inches under the force. You wont see the stretching of an optimum coupling spring or system in normal use. And you do not need to introduce additional elasticity in the harnesses, tuglines and ganglines.

But elasticity in the tugline and harness is not going to protect the dog in case of a collision; that is why I specified that shock rings attaching cable lines to the sled or cart are preloaded. They do not deflect under normal pulling conditons and therefore don’t interfere with coupling.

For more technical details related to this subject see another post:

https://everythingiknowaboutthatilearnedfrommysleddogs.wordpress.com/2012/10/20/sled-dog-mechanics-and-dynamics/

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