Duel Combustion Cycle Calculator

This calculator calculates equations commonly used for the Duel Combustion Cycles: ratio equations, efficiency and the mean effective pressure.
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The following are the variables for the equations.
V = the volume. i.e. V(1) is the volume at state 1.
r(k) is the compression ratio
r(e) is the expansion ratio
r(c) is the cut-off ratio
MEP = mean effective pressure. The constant theoretical pressure would produce the same network in one complete cycle if it acted on the piston. And can be defined as the following:
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MEP = Net Work For One CycleDisplacement VolumeMEP\ =\ \frac{Net\ Work\ For\ One\ Cycle}{Displacement\ Volume}MEP = Displacement VolumeNet Work For One Cycle​
η = the efficiency of the cycle
k = the adiabatic index
P = the pressure. i.e. P(1) is the pressure at state 1.
Where: P(1)[D(eff)-N(eff)] = Q(h)-Q(c), Q(h) is the amount of heat initially extracted, and Q(c) is the heat expelled.
Ratio CalculationsInputs﻿﻿V(1)
:150.00L​
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﻿﻿V(2)
:100.00L​
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﻿﻿V(3)
:200.00L​
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﻿﻿V(4)
:125.00L​
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﻿﻿V(5)
:75.00L​
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﻿﻿P(2)
:100.00atm​
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﻿﻿P(3)
:250.00atm​
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Output﻿﻿r(k)
:1.50​
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rk=V1V2r_k=\frac{V_1}{V_2}rk​=V2​V1​​
﻿﻿r(p)
:0.40​
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rp=P3P2r_p=\frac{P_3}{P_2}rp​=P2​P3​​
﻿﻿r(c)
:0.63​
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rc=V4V3r_c=\frac{V_4}{V_3}rc​=V3​V4​​
﻿﻿r(e)
:0.60​
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re=V5V4r_e=\frac{V_5}{V_4}re​=V4​V5​​
Mean Effective Pressure & Efficiency CalculationsInputs﻿﻿k
:25.00​
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﻿﻿Q(h)
:30.00kJ​
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﻿﻿Q(c)
:20.00kJ​
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Output﻿﻿MEP
:1.25​
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MEP=P1[Deff−Neff](k−1)(1−1rk)=Qh−Qc(k−1)(1−1rk)MEP=\frac{P_1[D_{eff}-N_{eff}]}{(k-1)(1-\frac{1}{r_k})}=\frac{Q_h-Q_c}{(k-1)(1-\frac{1}{r_k})}MEP=(k−1)(1−rk​1​)P1​[Deff​−Neff​]​=(k−1)(1−rk​1​)Qh​−Qc​​
﻿﻿η
:2.21​
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η Duel=1−rprck−1rkk−1(rp−1)+krp(rc−1)\eta_{\ Duel}=1-\frac{\frac{r_pr_c^k-1}{rk^{k-1}}}{(r_p-1)+kr_p(r_c-1)}η Duel​=1−(rp​−1)+krp​(rc​−1)rkk−1rp​rck​−1​​
In using the calculators and inputting values below, refer to Figure 1 and the different states of duel combustion cycles.
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Figure 1: Pressure vs Volume Graph for a Dual Combustion Cycle
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