Clarification of Onderdonk's Fuse Equation Assumptions

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Onderdonk's Fuse Equation is questioned for its accuracy in predicting the melting point of wires, particularly a 37 gauge copper wire tested at 3A, which did not break as expected. Key assumptions of the equation include the need for a sufficiently long wire to avoid cooling effects and the absence of any external cooling influences. The formula's parameters, such as area in circular mils and temperature in Celsius, are clarified, with suggestions to conduct experiments under varied conditions for better results. It is noted that the equation may be more applicable to thicker wires, and historical context reveals it was originally developed for high-voltage transmission lines. Overall, the discussion emphasizes the limitations of the equation and the need for conservative design practices in circuit applications.
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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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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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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.
 
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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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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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.
 
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.
 
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.
 
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.
 
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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
 

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