To help clear up any confusion when I talk about the “efficiency” or “efficiency score” of the bridges I build. This is a mathematical equation to determine how well a bridge performed.

Simply take the mass that the bridge held, and divide that by the mass of the bridge.

Mass held

________ = Efficiency

**Mass of bridge
**

Some confusion comes up when I weigh the bridge in grams while add weight to the bridge in pounds. These units do not have the same base, and cannot be divided against each other. I usually convert pounds to kilograms (1kg = 2.2 pounds) and then multiply the number of kilograms by 1000 to get grams.

So if my bridge held 54 pounds, I would convert that to kilograms. 54 pounds equals 24.54 kilograms. That equals 24540 grams.

To get the efficiency, I take 24540 and divide that by the mass of the bridge, which was, say, 33 grams. The efficiency score is then 744.

Just wondering, wouldn’t the span of the bridge have some bearing on the efficiency score of a bridge? ie if the bridge spanned a great distance, but wasnt as strong (but was strong enough) as a solid bridge of more mass which spanned a small distance, how would you compare them?

Kim, yes. All other things staying the same, a longer bridge will have a smaller efficiency score than a shorter bridge. I don’t know a good way add the length of the bridge into the actual efficiency calculation, but I do know that a longer bridge with a high efficiency score is more impressive than a shorter one.

I feel that efficiency score should be compated for bridges tested under same rules such as fixed spacing of support when being loaded.

However, if you want to include the span of the bridge (distance between supports) then that could be multiplied to the current efficiency score thus the larger bridge will get a multiplying factor that is directly proportional to the length to offset light smaller bridges and light tested over shorter span.

how do you find the mass of a bridge

Let me know if I got anything wrong. This is something I came up with to take span length into account with looking at efficiency.

The length of the bridge affects the efficiency score of the bridge in two ways.

(1) The mass of the bridge increases with span length.

(2) The force applied to structural elements per unit loaded mass increases with span length.

First, let’s change the Efficiency Score from measuring the Absolute Efficiency to the Relative Efficiency of a bridge.

Then let’s fix the Relative Efficiency Score of a bridge to be tested against a Reference Bridge.

For each bridge, we need to know its span, mass, and maximum load mass.

Let’s call these S, M, and L for the Reference Bridge, and s,m, and l for the tested bridge.

We want the Efficiency Score of a Tested Bridge to increase as the mass decreases and the maximum load mass increases, and to increase with span. That is to say:

Absolute Efficiency Score ∝ 1/mass,

Absolute Efficiency Score ∝ maximum load mass,

Absolute Efficiency Score ∝ span, and

Relative Efficiency Score = absolute efficiency score tested bridge / absolute efficiency score reference bridge.

Therefore,

Absolute Efficency Score ∝ (maximum load mass) * span/mass

Relative Efficency Score = Mls / mLS

= ls/(350 m)

Let’s use a solid wooden beam with dimensions 3.66cm x 3.66cm x 1m, with mass 1kg, and maximum loading mass 350kg as the Reference Bridge.

Then, Efficency Score = ls/(350 m).

Now, let’s try examining two bridges with our new formula:

(1) Balsa Bridge (https://www.garrettsbridges.com/wp-files/photos/science-olympiad/balsa-bridge/)

(2) Rising Starr Bridge (https://www.garrettsbridges.com/wp-files/photos/science-olympiad/booths-bridge/)

(All numbers are rounded to two significant figures.)

Since both bridges were Science Olympiad, we know that the span of the bridges is between 0.35m and 0.45m.

The Balsa Bridge’s mass 0.0081kg and the Rising Starr Bridge’s mass was 11g.

The Balsa Bridge’s maximum load mass was 13kg, and the Rising Starr Bridge’s maximum load mass was 15kg.

Thus,

13(0.35)/(350*0.0081) ≤ Balsa Bridge Relative Efficiency Score ≤ 13(0.45)/(350*0.0081)

15(0.35)/(350*0.011) ≤ Rising Starr Bridge Relative Efficiency Score ≤ 15(0.45)/(350*0.011)

Which is

1.6 ≤ Balsa Bridge Relative Efficiency Score ≤ 2.1

1.4 ≤ Rising Starr Bridge Relative Efficiency Score ≤ 1.8

I believe that with the extra so we could have built a bridge not only that could hold 20lbs for 2 minutes plus. We would have used better structural ability for the base and redone the side structure.

what is a decent efficiency for a bridge design?