What kind of figures did you want? And efficiency takes different forms.
Speed Efficiency is one. Energy Efficiency is another. Induction wins on both. Economic Efficiency is a factor. Which energy source wins depends on the cost per end kWh (remembering to apply energy efficiency to the equation).
Boiling a set volume of water on an Induction Hob is faster than a Gas Hob. That is definite. When I used the Induction Hob in my camper, I would set it to 400W, and by the time I got the teabag in the cup, milk out the fridge and sugar out, the kettle was boiling. On the Gas hob I would still be waiting.
Anyone can do a simple test ... Put a kettle on the gas ring, put an electric kettle on at the same time with the same volume of water and see which boils first. An Induction hob is extremely close to an electric kettle in terms of efficiency.
Do a search on the internet and you will find loads of tests carried out. Not specifically in a camper, but still Induction vs Gas
Example:
https://www.theguardian.com/food/2022/apr/05/whats-better-for-cooking-gas-or-induction-hobs
“It’s quick, efficient and you don’t get too hot while cooking, because it’s not throwing heat at you,” she says. “It’s also lower on energy, which everyone will now be needing.” On that point, Which? conducted a hob speed test last year, comparing the time it takes to boil a large pan of water: gas came in at 9.69 minutes and induction 4.81. But that’s not the only reason to consider induction. “There’s no point of ignition, so you don’t have to worry about things like frying pans catching fire,” Hayward says. Plus, it’s very controllable: “You can turn the power on or off, and expect a response in the pan within seconds.”
It is also fairly obvious TBH ... just think how much heat is thrown out into the air by a gas ring compared to an Electric ring. And an Induction Top is better still. First time I went away in my al-electric camper, the Chinese Diesel Heater wouldn't start (no shock there!). solution ... boil a kettle to make a couple of cups of Hot Chocolate. But not on the Induction stove. Instead get out the portable gas stove and use that. All the excess heat warmed up the van nicely.
If you want some figures ..... To raise a given volume of water to a given temperature, you need a given amount of power (Wh). It does not matter if the power is provided by Gas, Electric, or whatever.
Formula and example is here:
volume in litres x 4 x temperature rise in degrees centigrade / 3412
(4 being a factor and 3412 being a given constant)
for example 100 litres of water, to be heated from 20
ºC to 50
ºC, giving a temperature rise of 30
ºC would give –
100 x 4 x 30 / 3412 = 3.52
meaning that the water would be heated in 1 hour by 3.5kW of applied heat.
It's far more efficient to heat cookware directly instead of indirectly. Induction is able to deliver roughly 80% to 90% of its electromagnetic energy to the food in the pan. Compare that to gas, which converts a mere 38% of its energy, and electric, which can only manage roughly 70%.
So you are using over twice as much KWh of gas compared to Electric Induction to perform the same task.
The only question about if gas is more efficient is around the cost of the energy. And that depends on the setup.
Let's look at Campers specifically
You could say Gas is cheaper as you need to spend £xx on batteries to store the electric to then drive the Induction Hob. But bear in mind you would have to spend £yy on a gas installation to do the same. and who says £yy is less than £xx?
If you take it from the point of you have the infrastructure there and cost from that point, it is then a question of incremental costs. How much is a Calor Gas bottle in terms of energy?
6Kg Calor Bottle costs around £24. That bottle contains 85kWh of energy (6 x 14kWh). That works out to be 28p/kWh
efficiency is 38% so to get an effective 1kWh of energy "at the pot" costs 74p/kWh.
Let's say we are on EHU and charged 50p/kWh? that will cost between 55-60p/kWh "at the pot" - so Induction wins on cost efficiency as well as energy and speed. If off-grid and
Inverter, add in 10% for conversion inefficiency in terms of Energy efficiency, but cost comparision is tricky as it depends how the stored power was generated?
Solar? Free! B2B? bit of extra MPG maybe but minimal. Previous EHU? say 50p a kWh. Generator? Petrol contains 9.5kWh per Litre, so gross figure is 14.75p/kWh but how efficient is the conversion of petrol to 'transmitted' kWh to the 12V DC system? I think they are actually fairly efficient.
Interestingly, when you look at the following options, it is quite surprising ....
using LPG (via Bottles) for cooking is the most costly option compared to EHU or even a Generator. Once the infrastructure is in place, LPG is also more expensive than stored
battery power.
Is having a stored
battery infrastructure always more expensive than an LPG one? all depends. What needs to be included in the costing is also the applicance costs - a Gas hob is a couple of hundred pounds. An induction Hob is around £60. Gas Oven is a few hundred. Air Fryer is around £60 again. And of course a lot of the electric infrastructure will be installed regardless as a Leisure
Battery system is needed in a Motorhome.
