Hello Bertie and Dusty.
Manufacturers of movers will suggest having a large capacity leisure battery to run a mover for two reasons.
Firstly the construction of leisure batteries and their intended function is to provide a modest current over a long period, and to be able to withstand being left in a significant state of discharge for extended periods. This usually means their peak current capability is quite limited and that could compromise the operation of a mover. However it is generally the case that bigger leisure batteries also have bigger peak current capabilities
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The relationship between terminal voltage and the level of charge in a battery is not not linear It tends to flatten in the middle discharge section. Consequently the terminal voltage of a leisure battery that is 75% full, is not too dissimilar to the same type of battery that is only 25% full.
Mover manufacturers will be aware of these issues and will only be concerned if the terminal voltage falls much lower than this. To be fair if a battery voltage does fall that much then it points to a battery in a very low state of charge or even permanently damaged.
The second reason is that in most UK caravans, the battery also supplies power to lights and other appliances You therefore need a bigger battery as its serving these other services.
Dusty, I have re-read my posting, and I can't see how you have drawn those conclusions from it,. A linear relationship is one where the two related criteria are plotted on a graph the plotted points fall on a straight line. an inverse relationship can still be linear, it just the slope of the line means one criteria get small as the other get bigger.
But let me try to cover your points anyway; a battery is like barrel of water , You can deposit water , and you can take it out again. Consider if you put in 110 litres (Like a fully charged 110AH battery) You could withdraw money at the rate of 1L every hour and its fairly obvious the barrel would be empty after 110 hours.
You could withdraw could withdraw it at a rate of 110 litres per hour and the barrel would be empty after 1 hour. Batteries are in principle the same - but there may be practical limits to the maximum rate you can withdraw the current.
But with the barrel you could draw waster at a rate of 60 litres an hour but only do it for 5 minuets. that would be 1/12 of an our in which case you would only draw 1/12 of 60 litres which is only 5 litres, so the barrels capacity has only dropped by 5 litres.
I hope this helps.