Or, Robert McNamara, The Fog Of War, proportionality and “The One Horse Shay”
It’s the multimedia world; liven things up:
A fictional Deacon crafted this wonderful one-hoss shay in such a logical way that it could not break down. The shay was constructed from the very best of materials so that each part was as strong as every other part. In Holmes’ humorous, yet “logical”, twist, the shay endures for a hundred years then it “went to pieces all at once, and nothing first, — just as bubbles do when they burst.”
“Proportionality” is a more general expression of the principle which applied to airframe construction is referred to as “one horse shay.” An aspect of cost/benefit and risk management. In airframe structural design usually, for most elements, fatigue life (of aluminum components) is the overriding factor. Designing a structural element stronger and more durable than the other components in relation to stress and fatigue failures will add unnecessary weight which will cost thousands of dollars per pound in extra fuel for the life of the airplane .
In daily life we are doing a similar calculation weighing what we call priorities to allocate our money, time, attention, effort and energy…
Robert McNamara, one of the “Best and Brightest” JFK raised to leadership in the US government as Secretary of Defense, with 20/20 hindsight gives as an example of his own disproportionality, the Gulf of Tonkin incident that precipitated greater commitment to war with North Vietnam. Even if the alleged NVA attacks on a US destroyer occurred (they did not), no US sailors were injured, no damage to the vessel, only imaginary torpedoes thought to have been heard on sonar!
The slippery slope of disproportionality in structural engineering: in most (“statically determinate”) structures excess weight, stiffness and strength in one element will shift stresses to another part which then may require further increasing the strength and weight there…
When I was working at Boeing, 747 engineering was divided into Project and Stress departments. The Project engineers designed the plane specifying structure geometry, parts and dimensions, the Stress engineers analyzed the total structure to get stresses in each part/element turning these results back to Project engineers who modified the dimensions/weights according to the proportionality principles, stress in proportion to strength and acceptable fatigue life. Several iterations of this loop converged to the final design.
Above is an example of incorrect fastener type and location that raises the stress and caused failure via crack propagation. Aluminum sled components, and probably with most other materials too, breaking without any “plastic” (meaning residual) deformation is a fairly clear indication of an avoidable design and/or construction error. To put a positive spin on a bad situation, if there is no evidence of deformed material, no bend or twist that was not in the original part, only a fracture/break, then there is room for improvement to correct the error that led to the failure.
In Russia 20 years ago I talked to an aerospace factory manager at a time when they were being encouraged to develop markets for their products outside Russia. He could sell me Ti titanium runners bent to my specs with holes in the web for fasteners at the same price as Matrax. Sounds good? NOT. The export tax on Ti would have doubled or tripled that, then import duty would add more in USA. If an aluminum runner lasts ten years at least unless a design or construction error and Ti saves no weight and has no other performance benefit except resistance to particular damage that can be avoided, and costs 3-5 times Al, why waste money? That’s another application of the One Hoss Shay/Proportionality principle.
About putting a buffer piece between the stanchion bracket and the alu runner: The benefit depends on the stiffness/modulus of elasticity of the buffer material. For the front stanchion bracket (such as the first photo where the bracket was clamped on to curved section of runner) a material like stiff conveyor belting, say 1/4″ will compress and conform to the radius of the alu runner on the bottom and the straight bracket on top but will not carry/distribute any of the stress out beyond the edge of the bracket. This type of buffer does not need to be longer than the bracket. In contrast a 1/8″ UHMW pad between the bracket and runner is not going to conform/squeeze much because so thin and is not going to carry the stress very far past the bracket edge but no harm in making it 1/2 longer. I would guess (no exact calculation) considering the extremes, 1/4″ UHMW min 1/2″ longer on both ends would be a good compromise.
For the rear stanchion position I think preventing the break by eliminating stress raisers that act like notches to initiate crack failure is more important than having a thick piece of plastic to hold the broken runner together if it occurs. (Sometimes the function is also to raise the foot boards higher to prevent dragging and snagging.) As Einstein said, a smart man solves the problem, a wise man avoids it. The bracket and the runner are both straight (not curved) there. However that is the most highly stressed-in-bending location on most dog sleds, high centered and/or bridging on bumps in the trail, depending how much load is in the basket and how heavy the musher.
The idea is to move highest stress/strength ratio location on the runner back away as much as possible (even 1/4 inch will help) from the end of the stanchion bracket which is a discontinuity/stress raiser. A more elastic buffer piece/layer or pad can reduce the stress raiser effect at the end of a stiff bracket on top of the runner. The various “Easy Rider” sled designs with the rear stanchion farther forward move the position of that load away from the location of the highest bending load, the fulcrum of driver on one end and cargo on the other.
In high strength materials like this aircraft alu alloy cracks typically start at a stress raiser or notch or small surface discontinuity. And more often on the tension side in bending. High centered, the tension side is the top, bridging, the tension side is the bottom.Crack initiation and failure on the compression side of a “beam” is unusual but can happen. Compression failure starts with a crack at 45 degree angle from the surface. Bingo! Look at the top photo, compare to the next one below where the crack begins on one side at about 45 degree angle.
Here is an old style sled from 100 years ago, Scotty Allan’s racing sled.
Pins and bolts were avoided in this era. The rawhide lashing was typically attached through holes in the web similar to how holes in the web of an I beam are located to avoid stress raisers. The front stanchion is attached by lashing to the rear stanchion to form a solid truss (triangle) without any holes required at the junction.
Notice that the short stanchions are attached to the runners with lashing only on the back side. In my opinion that would make the sled more rigid with forward pressure on the driving bow but flexible when pulling back so that the front of the sled will respond to steering.
In the earlier posts you will find more discussion of fatigue, stress raisers, notch and crack propagation…