Help with analog gauge that has non linear resistance used to control needle

I am looking for ideas on how to “fix” a fuel gauge from a 1970’s vehicle that works on resistance from the fuel tank sender.

The gauge and sender work on 5V and the resistance, that the manuals state, are 10 ohms when full and 73 ohms when empty. This would indicate that in a linear fashion, half a tank would be about 40-41 ohms of resistance. With original parts no longer available, aftermarket senders are not calibrated in a similar fashion.

Test on aftermarket senders shows full at 10 ohms and empty shows 40 ohms, literally showing empty when the tank is half full (world problems right!). I am trying to figure out a way to take the ohms from the new fuel sender and convert them to the ohms, listed in the manual, so the gauge works correctly. The way it is configured is the gauge receives 5v, from a voltage limiter, and this runs to the sender that inputs the resistance before going to the ground.

My thoughts were to use a microcontroller to do the calculations but I’m unsure how this could be accomplished or what components to use. I still would like to use the old gauge and not convert it to digital. Hoping there is a simpler way that someone can suggest.

You say that with the new sender "Test on aftermarket senders shows full at 10 ohms and empty shows 40 ohms, literally showing empty when the tank is half full (world problems right!)." It seems to me that this sender would indicate 1/2 full when the sender is on the empty position (40 ohms) as this corresponds to rouighly 1/2 full on the original sender? Please confirm?
Usually the gauges are linear (they're fairly standard meters) but the senders are not, as they work with an arm on a float. The markings on the gauge are usually adjusted for this, ie the gauge scale is not linear.
Please confirm above and I'll try and figure out a way to solve this.

Thank you for the reply!
You are correct the fuel sender has a float and a bendable wire. When the float is up and it hits the stop it reads 10 ohms, when the float is at the bottom and hits the stop it’s at 75 ohms. When I re-read what I wrote, based on your comments, I can see what you were saying and it doesn’t make sense. I tested the fuel gauge and the needle indicates full when applying 10 ohms and empty when using a 47 ohm resistor. I tried a 22 ohm resistor and it just under half. When I tried 32 ohms it was just above empty.

I should also mention that most Ford’s and Mopar’s use a cvr (constant voltage regulator) to take 12v down to 5-6v by using a heated wire and contacts that open and close in an attempt to average or pulse the voltage. Obviously a problem and when I was testing, the numbers were 4-6v inconsistently. So the numbers listed are quite variable.

Based on this, I can see the easiest solution would be to put a new stop on the sender, where the resistance is correct, and bend the float down until it is at the bottom of the tank. However since I have started this journey I have also discovered that the temperature and oil pressure gauges work on the same set of values, 10 and 73 ohms, according to the manual. I’m still interested if there is a way for a mcu to read the ohm values, from a sender, and output different ohm values that would correspond to the gauges. As an example, a mcu would read 40 ohms from the sending unit (half full) and output 25 ohms to the gauge which should be roughly half a tank.

This is where I am at. I don’t know if a mcu is the best choice, that’s why I’m looking for some guidance on which direction to go. Again, Thank you for the reply, I do appreciate it!!! Btw, this is a very common problem amongst car enthusiasts and any help would be appreciated by all of us.

A lot of old fuel sensors had a bare restive wire that was wound on an insulator in a non linear fashion, similar to a wire wound potentiometer. There was a connection to one end of the wire and a slider mechanically connected to the float in the tank. The non linearity was an attempt to make the resistance output between the slider and connected end of the wire match the non uniform cross section of the fuel tank. The accuracy still wasn't that great, and very sensitive to the tilt of the tank as the car was driven arount. This system was typically only used in more expensive vehicles. Gas gauges for the cheaper vehicles, commonly referred to "American" type, just used a fairly linear resistance vs fuel depth. These were only accurate at full and empty and could vary by a lot (e.g.+/- 1/8 tank) in between. Commonly, you could fill up the tank and drive for dozens of miles before the gauge would even start to drop.

I suggest simply digitizing the voltage output of your new replacement sensor, couple that digital number to a lookup table and convert the output of the LUT back to analog. No particular speed is needed and a 16 bit system will give decent accuracy. Programming the LUT will be a bit of work and might require a few experiments but if enough effort is made it will be reasonably accurate.You could replace the LUT with some sort of processor executing a simple program that in effect implements an LUT. Just pick a number of breakpoints and perform a linear interpolation between them, e.g between Voltage A and Voltage B, output 2/3 of the input voltage, etc.

Thank you for the suggestion. I am still working on the gauge but your idea seems like a very plausible solution. I need to do some more research into the programming aspect but your idea has spurred some ideas that I will investigate further Thank you for taking the time to respond, I do appreciate it!!!

Hi, sorry I have been so long..... busy....
Had a long think about this. Apart from digital ways to do this, there are no easy ways to do it with analogue circuitry that I can think of.
SO.... can't you fix the old one? They're usually mechanically fairly simple and barring wholescale corrosion or something like that, it should be fixable.
The other approach you could take is to rewind either resistance element to give you the resistance you need. This would need a bit of calculation as to the length of wire needed and the resistance in ohms per foot/meter to get it right, and you'd have to find the right resistance wire to do it. Or maybe you could put the old element (if still good) on the new gauge hardware?
It's a difficult one but I think the repair coiurse is worth looking at?
Cheers

In summary, older fuel sensors had non-linear resistive wires that attempted to match the irregular shape of fuel tanks but weren't very accurate. Cheaper vehicle gauges were typically only precise when the tank was full or empty.

For a solution, I recommend digitizing the output of the new sensor, using a lookup table (LUT) to convert it back to analog form. This method can provide reasonable accuracy. Alternatively, you can use a processor with a simple program that emulates a LUT by performing linear interpolation between defined breakpoints.