I think I may have been slightly less than clear on the point, I meant current is less than causes fault type disconnection. Sorry if anyone was confused.
There is a severe mathematical problem plotting things on logarithmically scaled graphs (and we do it a lot for all kinds of things) in that the reason to use these scales is that they in many applications allow us to plot a straight line, which we can the use. It doesn't work for fuses or MCBs does it? Whoever chose to use this scaling has not really been very helpful, they need to calculate the underlying function they wish to plot and scale the axis using a suitable function. There is no need for this to be a log, exponential, or any other easy curve. It may mean they need to make their own graph paper but this is trivial nowadays with computers.
Now fuses, as excellently described by Mike follow an I²t heat characteristic whilst adiabatic and will need some heat loss correction at longer times. It would seem that the fuse plotted on log time against a log square law current might produce a fairly straight line. Log current is probably incorrect, and so the graphs are curved.
The MCB also depends on heat, but well outside the adiabatic region, so the current axis will be a modified square law, probably a square plus a thermal loss part which will be probably connected to temperature to a fourth power and an operating environment offset in absolute temperature. The magnetic part has a threshold, the ampere-turns to cause disconnection, and another factor of current controlling the acceleration of the contact mechanism, so energy let through.
Whilst various kinds of curve fitting can improve the situation, a straightforward equation is the way to go for accuracy, but probably not for general electrical use. It is unlikely that a discrimination study needs more than the equation, after all, there are more factors, such as how many times a fuse has been stressed before, which will have an effect on the real performance. It is likely that we have these graphs because no one has thought it worth the effort to produce linear lines, and in fine detail, it might be quite difficult. Curve fitting is, in my view, a dangerous game unless the underlying characteristics are known, various kinds of regression analysis should be most accurate if the degree is chosen to match the underlying characteristic, but then determining this is difficult as I say above. B-splines or other spline types have all kinds of nasty end effects and become complicated to use when end connection slopes are taken into account. Linear interpolation of a curve is pretty poor, one takes one's pick depending on the effort and time available.
I think I may have been slightly less than clear on the point, I meant current is less than causes fault type disconnection. Sorry if anyone was confused.
There is a severe mathematical problem plotting things on logarithmically scaled graphs (and we do it a lot for all kinds of things) in that the reason to use these scales is that they in many applications allow us to plot a straight line, which we can the use. It doesn't work for fuses or MCBs does it? Whoever chose to use this scaling has not really been very helpful, they need to calculate the underlying function they wish to plot and scale the axis using a suitable function. There is no need for this to be a log, exponential, or any other easy curve. It may mean they need to make their own graph paper but this is trivial nowadays with computers.
Now fuses, as excellently described by Mike follow an I²t heat characteristic whilst adiabatic and will need some heat loss correction at longer times. It would seem that the fuse plotted on log time against a log square law current might produce a fairly straight line. Log current is probably incorrect, and so the graphs are curved.
The MCB also depends on heat, but well outside the adiabatic region, so the current axis will be a modified square law, probably a square plus a thermal loss part which will be probably connected to temperature to a fourth power and an operating environment offset in absolute temperature. The magnetic part has a threshold, the ampere-turns to cause disconnection, and another factor of current controlling the acceleration of the contact mechanism, so energy let through.
Whilst various kinds of curve fitting can improve the situation, a straightforward equation is the way to go for accuracy, but probably not for general electrical use. It is unlikely that a discrimination study needs more than the equation, after all, there are more factors, such as how many times a fuse has been stressed before, which will have an effect on the real performance. It is likely that we have these graphs because no one has thought it worth the effort to produce linear lines, and in fine detail, it might be quite difficult. Curve fitting is, in my view, a dangerous game unless the underlying characteristics are known, various kinds of regression analysis should be most accurate if the degree is chosen to match the underlying characteristic, but then determining this is difficult as I say above. B-splines or other spline types have all kinds of nasty end effects and become complicated to use when end connection slopes are taken into account. Linear interpolation of a curve is pretty poor, one takes one's pick depending on the effort and time available.
