Temperature independent fuel mixing

Making fuel with a gas mixer set to 33:67 works fine when the incoming O2 and H2 have the same temperature. But when the temperature is different, the mix will become incorrect.

To get a perfect fuel mix regardless of the temperature difference, a circuit can be used to calculate which gas mixer setting to use. The gas mixer will accept decimal values, so it's incredibly accurate. This allows it to always make a perfect 1:2 mix. Just don't forget that making hot fuel will lead to explosions, if that should happen, please enjoy the strongest and most perfect explosion possible.

Components needed:

• 3 logic I/O (2 readers, 1 writer)
• 4 logic processor (all math)
• 3 logic memory
• 2 pipe analyzer
• 1 gas mixer

Build:

This part will turn the following equation into a circuit, it will only work when the H2 pipe is connected to input 1(the side)
gas mixer setting = 100 / ( 1 + Temp.oxygen/(2*Temp.volatiles) )

• Connect the H2 pipe to input 1 (side) and O2 pipe to input 2 (top)
• 2 pipe analyzers
  • On the O2 and H2 sides
• 2 logic readers
  • Read the temperatures of the pure O2 and H2
• 4 math and 3 memory units for calculations
  • A = 2*Temp.volatiles
  • B = Temp.oxygen/A
  • C = B+1
  • D = 100/C
• 1 logic writer to send the result to the gas mixer
  • The gas mixer will accept decimal values, so the mix will be a perfect 2:1 mix of H2 and O2

Extra:

• If the O2 pipe connects to input 1 (the side) instead, the equation to use is
  • gas mixer setting = 100 * ( Temp.oxygen / (2*Temp.volatiles) ) / ( (1 + Temp.oxygen / (2*Temp.volatiles)) )
    
• Use a PAC or Transformer to put this circuit on it's own data network
• The circuit will require 170W on standby and 270W while mixing fuel

The fun math part that everyone will read

The ideal gas law, the chemical formula and some understanding of the gas mixer is all that's needed to find the desired equation

• PV=nRT
• 1 O2 + 2 H2 -> products

We want one expression for oxygen and another for volatiles, .o and .v will be used to indicate if it's oxygen or volatiles

• oxygen: P.o*V.o = n.o*R*T.o
• volatiles: P.v*V.v = n.v*R*T.v

The chemical formula tells us how n.o and n.v are related, n.v is twice the value of n.o, so we can remove the .o and .v by replacing them with n again

• n.o = n
• n.v = 2n

Now we will use this to solve both expressions for n

• oxygen: n = P.o*V.o / (R*T.o)
• volatiles: n = 1/2 * P.v*V.v / (R*T.v)

Combine the expressions

• P.o*V.o / (R*T.o) = 1/2 * P.v*V.v / (R*T.v)

We now cancel R from both sides. We can also remove P.o and P.v because the gas mixer is already compensating for differences in incoming pressures and we don't want to do that twice, this leaves us with

• V.o/T.o = 1/2 * V.v/T.v

The gas mixer can only influence the volume, not the temperature, so we will solve for the volume ratio

• V.o/V.v = T.o/(2*T.v)

The V.o/V.v ratio has no unit, it's just a number. So we can replace it with the settings on the gas mixer, because the value itself is unchanged from doing that

• 1) Ratio.o/Ratio.v = T.o/(2*T.v)

This is our first equation.
We now have two unknowns, Ratio.o and Ratio.v, and one equation. The gas mixer can give us another equation, looking at the input values of it tells us that it accepts values between 0 and 100, it even takes decimal values if the Labeler is used which is great, it means there won't be any rounding errors in the fuel, it will really be a perfect 1:2 ratio. Treating 100 as 100% means ratio.o and ratio.v makes more sense to use, we can just multiply with 100 at the end to give the gas mixer the value range it wants, doing it this way means we can avoid some clutter so the formulas are easier to read

• 2) Ratio.o + Ratio.v = 100% = 1

Two equations, two unknowns. This can be solved.
Lets do calculations for both Ratio.o or Ratio.v, the end result is the same but the formulas and which pipe goes where will be different.

First lets solve for Ratio.o

• Ratio.v = 1 - Ratio.o

now substitute this into the first equation

• Ratio.o/(1-Ratio.o) = T.o/(2*T.v)

After some algebra we get

• Ratio.o = T.o/(2*T.v) / (1 + T.o/(2*T.v))

To make it easier to look at, lets substitute T.o/(2*T.v) for k

• Ratio.o = k / (1 + k)

Now we will multiply with 100 to get a value between 0 and 100 which the gas mixer wants.

• gas mixer setting = 100 * T.o/(2*T.v) / (1 + T.o/(2*T.v))

This is the final equation when O2 connects to input 1, the result will be sent to the gas mixer

Secondly lets do Ratio.v

• Ratio.o = 1 - Ratio.v

now substitute this into the first equation

• (1-Ratio.v)/Ratio.v = T.o/(2*T.v)

After some algebra we get

• Ratio.v = 1 / (1 + T.o/(2*T.v))

To make it easier to look at, lets substitute T.o/(2*T.v) for k

• Ratio.v = 1 / (1 + k)

Now we will multiply with 100 to get a value between 0 and 100 which the gas mixer wants.

• gas mixer setting = 100 / (1 + T.o/(2*T.v))

This is the final equation when H2 connects to input 1, the result will be sent to the gas mixer

As it turns out, the Ratio.v equation is shorter and choosing that one means one less math operation.