Hello gary and Gybe,
There is a flaw in your thinking gary, based on the manufacturers figures of 22 mins for 55C rise for 13L may mathematically give your 2min per litre, but under heating there are considerable thermal convection currents inside the tank which means you don't just heat the top 1 litre, the whole 13L tank starts to warm up. Its not perfectly evenly distributed there will be some hotter water at the top but the temperature gradient from top to bottom under heating will be much less than 70 to 15C you suggest.
The thermal currents inside the tank are driven by the heating effort and with 1.25kW gas input (approx 1kw into the water with about .25kW heat losses through the flue assuming an 80% efficiency) and 1.5kW electric a total 2.5kW heating will cause quite some mixing.
The first litre of water will only reach a super elevated temperature provide no water is drawn off. This is through stratification which can only occur when the water in the tank is largely undisturbed. So after a couple of minutes you may have water at the top of the tank which is several degrees warmer than the bottom, BUT as soon as you start to use the water in the heater the inrush of cold water very quickly starts to mix the whole tank and it starts to assume a more even but lower temperature.
Hi Gybe, I agree the heater will continue to try raise the water temperature even when water is being used, and it is quite true the warmer the water on entry, the less energy is needed to raise its temperature to the desired level, but shower usage typically between 3 to 4 Litres a min. this still rapidly out strips the heaters ability to maintain the desired water temperature.
The concept of storage water heaters and showers, relies on the fact that water from a fully heated tank is too hot to use undiluted. Typically the top temperature of a heater is 68 to 70C and a common shower temperature is is roughly 40C the shower mixer tap allows the user to proportion the amount of hot and cold water to achieve the comfortable shower. 13 Litres of water at 70C is roughly capable of providing enough hot water for three showers when mixed with cold water. - the biggest problem is water storage both of fresh cold and waste.