By Todd M. Bennett P.E.
A while back I was reading my Newf News, the official newsletter of the Newfoundland Dog Club of Canada. Peter Maniate writes “Carting Corner”, a regular column in Newf News, which is filled with all kinds of equipment information and training tips about draft work with your dog. This particular column was entitled “The Pull Factor” in which he described the fact that there is a certain amount of force, per amount of weight of a vehicle, required to move that vehicle. This number is constant for a given vehicle and shows that doubling the weight of any vehicle would double the required force to pull that vehicle. This sounds simple enough, but determining the pull factor of different vehicles removes the weight of the vehicle from the equation and allows us to compare these vehicles in terms of required pull, regardless of weight. This data is critical in understanding draft equipment and how it relates to your dog and the environment in which you are working. Peter 's observations, as well as my own, follow:
Weight is merely a measurement of gravitational force and, here on earth, pounds of weight are equivalent to
pounds of force. Therefore, this “pull factor” is described as a simple percentage ratio:
Pull Factor (ratio) = Pull Force (pounds) / Weight Force (pounds) x 100
The Pull Force can be measured using a common fish scale – the type with a hook on the end that, when pulled, compresses a spring inside and indicates the weight of the fish in pounds. When pulled horizontally, attached to a draft vehicle, the scale then indicates the force required to move the vehicle. The Weight Force is easy to measure also – just weigh the vehicle AND its load using a bathroom scale (or anything equivalent that is large enough to accommodate the objects).
Peter started on a flat paved surface where he discovered that his cart, which weighed 107 pounds loaded and has 20” wheels, required 2 pounds of starting force to get the cart moving and 1.5 pounds of pulling force to continue the carts movement at a constant speed. This equates to a Starting Pull Factor of 1.87 (or 1.87 pounds of pull force for every 100 pounds of cart weight) and a Maintenance Pull Factor of 1.4. He then tried his wagon, which weighed 132 pounds loaded and has 10” wheels. He measured 13 pounds (9.8 Pull Factor) to just start it moving and 9 pounds (6.8 Pull Factor) to maintain movement.
He then tried this same experiment with the same cart and wagon on different terrain and the Pull Factors he calculated are listed in the following table:
Upon casual inspection of the data several things become obvious. The cart was easier to pull than the wagon was, even if they weighed approximately the same! A paved or smooth, flat surface is considerably easier on your dog than rougher or hilly surfaces. Peter concluded that if you want to train on hills or rough surfaces, start your dog out with less weight or an empty cart and give him more frequent breaks.
Now I want to take his results one step further. Peter did not (and did not need to) take measurements on every conceivable draft vehicle in every conceivable situation you might encounter while carting with your dog. He provided enough information to give us a basic understanding of the “Pull Factor” principle and I want to extend that knowledge to allow you to extrapolate his findings in your own mind when encountering other equipment and terrain.
There are several pulling forces that are exerted by the dog when pulling. As described earlier, there is the starting force (force required to start the vehicle moving) as well as the maintenance force (force required to keep the vehicle moving). The starting force is the force required to overcome the inertia of the object. The maintenance force is the force required to overcome gravity (from the earth’s pull on us) and various sources of friction.
Inertia has an effect on how easily a vehicle starts to move upon initial pull from the dog. Physics tell us that once inertia is overcome, without any other forces acting on the vehicle, it would stay moving at a constant speed without any more pull from the dog. But we know that there are other forces acting on the vehicle, namely friction and gravity. Therefore the dog is required to continue pulling on the vehicle to overcome these other forces, but the required pulling force drops after the vehicle starts to move and the effects of inertia are overcome. Inertial force is directly proportional to the weight of the vehicle.
Gravity is exerted on the vehicle by the earth and is minimal or negligible on flat surfaces because the pulling force (horizontal) is not exerted in the same plane as the gravitational force (vertical). When pulling up or down hills, however, the gravitational force becomes a “force to reckon with”. Gravitational force is directly proportional to the weight of the vehicle.
Friction comes in two types: that which is caused by the design of the vehicle (internal) and that which is caused by the surfaces the vehicle comes in contact with (external). Internal friction is caused from the contact of wheel bearings on the shaft and the surface characteristics of the wheels, or the surface characteristics of runners on a drag vehicle like a travois or sled. External friction is caused from the surface characteristics (roughness, stickiness, etc.) of the ground.
Just like the dog exerts a pulling force on the vehicle when he is pulling, the vehicle exerts a braking force on the dog when stopping or when the force of gravity is greater than that of friction (going down hill). Remember what I said about inertia: the object tends to stay in motion unless acted upon by an outside force. Therefore, there is a required minimal force to be exerted by the dog in order to stop the vehicle, which is proportional to the inertia (weight). Frictional forces also have an effect on how easily (or not) an object comes to a stop. A vehicle that requires more frictional force to keep moving would exert less braking force on the dog when stopping. The opposite is true for a vehicle that requires less frictional force to keep moving. Finally, we all know that a vehicle being pulled uphill exerts more gravitational force and is very easy to stop, and the opposite is true for a vehicle being pulled downhill.
Even though the wagon weighed only 1.24 times the cart, the wagon took over 5 times more force to start it moving on a flat surface! Since gravity has a negligible effect on a flat surface, and the differences in inertia (weight) of the two are minor, there must be a considerable difference in the friction. This is evidenced by the fact that the required maintenance force for the wagon is also nearly 5 times that of the cart. This does not tell us whether the friction is internal or external, however. Looking a little further, we see that the wagon took only about 2 times more force than the cart in the grass. This shows that the external friction of the rough, grassy surface becomes more of a factor compared to the internal friction of the vehicle, making the pull factors more equal to one another. When we go to a sloped surface, the gravitational force on the vehicle becomes even more of a factor compared to the internal and external frictions, making the pull factors of the wagon only about 1.3 times that of the cart.
With a maintenance pull factor of 1.4 on pavement and 3.7 on grass, it would take the same force (4 pounds) to move the cart weighted to 285 pounds on a smooth, flat surface as it would to move the original 107 pounds on a rough, grassy surface! But the calculations show that it would take the same force (13 pounds) to pull a 190- pound wagon on pavement as it did the original 132 pounds on grass. The fact that the weight change is smaller on the wagon example than on the cart example shows that the wagon is less affected by the change in external friction between the two surfaces. This continues to show that the difference between the cart and wagon is caused by a large difference in internal friction.
Lets start with the first force that has to be overcome: inertial force. Remember that this force is proportional to the weight of the object. It doesn’t matter if you are going uphill, downhill, or across a flat, and is only a factor when initially starting or stopping. The second is frictional force. This force has to do with how the object is constructed and what surface you are pulling it on. It also doesn’t matter if you are pulling up or down hill; the frictional force remains the same. The last is gravitational force. This force is like inertial force in that it is proportional to the weight of the object, but unlike inertial force, its affect remains even after the vehicle is moving. This is also the only force that changes as the slope of the terrain changes.
We determined that the wagon was harder to pull because it had more internal friction to overcome than the cart. This is due to the fact that the cart had 2 narrow 20” bicycle wheels and the wagon had 4 wide 10” wheels. First, it is probably a safe bet that the bicycle wheel hubs are built for speed and the wagon wheels for durability. This might equate to less bearing friction in the bicycle wheels, plus there are only 2 of them. Second, the 2 narrow cart wheels would have considerably less surface contact with the ground than the 4 wider wagon wheels, resulting in considerably less surface friction. Surface friction is usually more of a factor than bearing friction. Taking this further, we can infer that dragging a vehicle (like a travois or sled) would require even more maintenance force to overcome the added friction. Just think of how much harder it would be to drag 100 pounds than it would be to roll it! Lastly, the 20” wheels would simply be easier to rotate than the 10” wheels, but the physics involved is too complicated to get into here.
Now lets talk about external friction. Take a cart, which has considerably less internal friction than a sled, and put it in the soft snow. We’ve just added a large amount of external friction to the cart because it sinks into the snow. However, the slippery characteristic of the sled bottom (internal friction) against the compacted snow (external friction) is much less than the wheels sinking into the snow. Likewise, the cart would stop very quickly when the dog stops and the sled would want to keep moving, exerting more stopping force on the dog. Not to mention the fact that the sled would want to slip downhill if the dog was traversing across a slope (gravitation and friction)!
Gravitational forces are the ones we all seem to be concerned about. We’ve all heard someone say, “I think that’s too much weight for the dog”. Because gravitational force is directly proportional to weight, we have a good grasp of the effects of putting more weight on the vehicle. But remember, gravitational force has minimal effect on the vehicle on a flat surface (however, it somewhat influences the frictional forces that are applied to some vehicles). We saw that as we moved to a 45-degree slope, the cart and wagon pull factors became more equal. Therefore, we can infer that if we could stand the dog on a vertical wall and have him pull straight up, the pull factors would virtually be the same, as friction becomes negligible and the dog now starts to pull directly against gravity!
As you can see, these forces get very complicated when they are all acting on the vehicle and the dog at the same time. But applying these basic principles to your selection of draft equipment is imperative when deciding which is going to be easier for your dog to pull under various circumstances.