Clarification of Onderdonk's Fuse Equation Assumptions

In summary, Onderdonk's Fuse Equation is an approximate formula that was developed to determine the minimum wire size needed to carry a short-circuit for a certain amount of time. It assumes no cooling and a short time period before the wire reaches its melting temperature. The equation may not accurately depict the behavior of thinner wires, and other factors such as airflow and insulation can affect the results. This equation was originally developed for high-voltage transmission lines and dates back to at least 1928.
  • #1
tempneff
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3
Hi all,

I am trying to get an understanding of Onderdonk's Fuse Equation:

##I_{fuse}=Area*\frac{\sqrt{log\left(\frac{T_{melt-T_{ambient}}}{234-T_{ambient}}+1\right)}}{33*Time}##

Empirically I do not see that this function accurately depicts the behavior of the wires I am using. For example, I hooked up a 37 gauge copper wire to a current source with 3A. I verified the values in this chart of Onderdonk's values for copper against the equation and found that they agree. I should have seen the wire break within a second, however it glowed but did not break. It took nearly 5A to melt it.

I'd like to know what assumptions were made for this equation to work? Such as length of wire, ambient pressure maybe...

Thanks in advance, I love this site.
 
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  • #2
What units did you use for the area and for the temperature parameters?

The wire needs to be sufficiently long so that the middle section is not cooled by the mounting connections.

Forced or convective airflow will cool the wire and so require higher currents before fusing. I do not know the original airflow assumption.

A ceramic or glass tube will reduce thermal radiation and lower the current needed to fuse the wire. You would need to correct the Tambient if in a tube to the temperature of the tube inside wall.
 
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  • #3
Temperature is in Celsius, area is in circular mils. I didn't think to try longer wires, I have been using wires I thought would be comparable to standard electronic fuse ~3/4 inch.
 
  • #4
tempneff said:
Hi all,

I am trying to get an understanding of Onderdonk's Fuse Equation:

##I_{fuse}=Area*\frac{\sqrt{log\left(\frac{T_{melt-T_{ambient}}}{234-T_{ambient}}+1\right)}}{33*Time}##

Empirically I do not see that this function accurately depicts the behavior of the wires I am using. For example, I hooked up a 37 gauge copper wire to a current source with 3A. I verified the values in this chart of Onderdonk's values for copper against the equation and found that they agree. I should have seen the wire break within a second, however it glowed but did not break. It took nearly 5A to melt it.

I'd like to know what assumptions were made for this equation to work? Such as length of wire, ambient pressure maybe...

Thanks in advance, I love this site.

It could be worth while,doing the experiment with the wire under various conditions - enclosed in a tube, wrapped in fibreglass etc. to find when you could actually achieve fusing. You may have been 'borderline' with your test, even though the dissipated power at 5A is 25/9 times the power with 3A (approx) - which doesn't look to be very borderline, I admit.

If you are doing these experiments with a view to actually applying the results for a circuit design, it would be wise just to work on recommended practice, which is much more conservative. Alternatively, if you want to make a fuse, then I believe Tin is the preferred metal.
 
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  • #5
Looks like this is an aproximate formula and 37 gauge is very thin. Maybe, the formula better aproximates melting of thicker wires?
 
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  • #6
First, the formula is incorrect. The " 33*Time " should be under the square root radical. Second the denominator 234-Ta should be 234+Ta. The two primary assumptions are (a) no cooling, not from convection, conduction, nor radiation (Thus rapid heating assumption), and (b) time is the time TO the melting temperature, not that plus the time to actually melt the copper. Thus, the relevant time is short, from one to 10 seconds, depending on who you read.
 
  • #7
As a bit of theory, this is interesting but, if a fast fuse action is needed in practice, there are many better ways of doing it.
I'd bet that all that work was done before the luxury of alternatives was available for protecting sensitive stuff.
 
  • #8
Actually, Onderdonk was considering the copper wires that supported the poles and insulators of high-voltage transmission lines. He wanted to determine the minimum wire size necessary to carry a short-circuit for a time period long enough for the circuit protection devices to kick in. His equation dates back no later that 1928. We have found no references earlier than that.
 
  • #9
DGBUCAD said:
Actually, Onderdonk was considering the copper wires that supported the poles and insulators of high-voltage transmission lines. He wanted to determine the minimum wire size necessary to carry a short-circuit for a time period long enough for the circuit protection devices to kick in. His equation dates back no later that 1928. We have found no references earlier than that.
Hmm, but I would think that melting point of wires is much above allowed termal stress of the insulators.
 
  • #10
The problem was arcing across the insulators because of dust or moisture. Here is where this is discussed: E. R. Stauffacher, “Short-time Current Carrying Capacity of Copper Wire,” General Electric Review, Vol 31, No 6, June 1928
 

1. What is Onderdonk's Fuse Equation?

Onderdonk's Fuse Equation is a mathematical equation used to predict the velocity of a projectile based on the length of the fuse and the time it takes for the projectile to detonate after the fuse has been lit. It was developed by American engineer Lewis Onderdonk in the mid-1800s.

2. What are the assumptions made in Onderdonk's Fuse Equation?

The assumptions made in Onderdonk's Fuse Equation include a constant burn rate of the fuse, a constant acceleration of the projectile, and no air resistance. It also assumes that the fuse is perpendicular to the trajectory of the projectile.

3. How accurate is Onderdonk's Fuse Equation?

Onderdonk's Fuse Equation is considered to be fairly accurate for short-range projectiles, but it becomes less accurate for longer ranges due to factors such as air resistance and variations in the fuse burn rate. It is often used as a starting point for more complex projectile motion calculations.

4. Can Onderdonk's Fuse Equation be applied to all types of projectiles?

No, Onderdonk's Fuse Equation is specifically designed for spherical projectiles such as cannonballs. Other types of projectiles, such as arrows or missiles, have different factors that must be taken into account in their equations.

5. How is Onderdonk's Fuse Equation used in modern times?

Onderdonk's Fuse Equation is still used in some military and historical settings, but it has largely been replaced by more accurate and complex equations in modern projectile motion calculations. However, it is still a valuable tool for understanding the basics of projectile motion and can be a useful starting point for more advanced calculations.

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