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Name: Scott S.
Status: Other
Age: 30s
Location: N/A
Country: N/A
Date: N/A


Question:
I am trying to calculate delivery efficiencies for our fleet of trucks, and we have equations to calculate cost from point A (the terminal) to point B (the customer). That's all well and good for two dimensional thinking. What I would like to do is to incorporate altitude changes into the equation.

For instance, if point A is at Sea Level, and point B is at an elevation of 1000 feet, I would like to find the difference in cost per mile. In other words, what is the diffenence between the cost if point A and B were both as sea level as opposed to being 1000 feet different?



Replies:
Scott,

I really do not know of an equation which could quantify this...my suspicion would be that fuel cost and time for the delivery would be the best way to calculate this. Note that travel vertically will add a time component to delivery beyond the normal horizontal travel. Because one might or might not encounter red lights when travelling, it would be quite difficult to specifically quantify a component due to 'vertical' travel.

If I were trying to quantify this, for example, to estimate delivery costs and to set prices for customers, I would gather data about current deliveries. You could record distabce between points a and b (the horizontal component), fuel used for the delivery (this could be hard to estimate depending on the sensitivity of your fuel gauge), and time required for the delivery. A notation could be placed on the records to indicate a change in elevation. By gathering this data, you could determine predicted miles-per-gallon while climbing and/or travelling at (approximately) the same elevation and then set your rates based upon a elevation map for your delivery area. As always, mathematics is only an approximation, but you should be able to predict, for a given delivery to a particular area, what the predicted cost would be.

Thanks for using NEWTON!

Ric Rupnik


I assume that you calculate the cost by determining a certain cost per mile [$/mile] and multiplying by the distance from A to B. Algebaically, you are calculating the distance from A to B by putting the points on an X-Y graph, say (xB, yB) and (xA,yA) and calculating the distance between them using the Pythagorean Theorem:

D = { (xB-xA)^2 + (yB-yB)^2 }^1/2

To generalize this to take altitude into account you have to know the difference in the altitude of B and A, call the altitudes zB and zA respectively. Assign a cost per mile between zB and zA, keeping in mind that the cost per mile will be positive if you are going 'up hill' and negative if your are going 'down hill' . Then the distance formula just adds another term for the difference in altitude using the Pythagorean Theorem with three terms:

D = { (xB-xA)^2 + (yB-yB)^2 + (zB-zA)^2 }^1/2

Vince Calder



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