Talk:Mean effective pressure

Talk:Mean effective pressure
Discussion and changes made on 2008 Oct 13.

The display of the symbols in the formula creates an unintended appearance. The combination of an italicized "T" and the adjacent "/" appear to be a italicized upper case "Pi". A copy for the formulas without the italics is correct.
 * MEP = 2 πT/V for a two-stroke,
 * MEP = 4 πT/V for a four-stroke

The text was edited to add spaces and consistently use italicized text in the formulas. Unless there is some reason, it seems that the use of italicized text does not serve a useful purpose and should be deleted.

I have made several other revisions/additions to clarify the description of MEP and to add the theoretical basis for MEP. A purpose of this Talk is to document the changes made for others to consider and offer further improvements.

The article can be improved if a general description of the principles and theory is added in the first paragraph. The following was added after the first sentence:


 * Mean Effective Pressure is defined as the average pressure that the gas exerts on the piston(s) through one complete operating cycle of the engine. This definition can be expressed in terms of the work per operating cycle as
 * Work Per Operating Cycle = (Mean Effective Pressure) x (Swept Volume per Operating Cycle)


 * Since the work per cycle can also be expressed in terms of torque, the work equation becomes
 * (Torque) x (2 π Revolutions per Cycle) = (Mean Effective Pressure) x (Swept Volume per Operating Cycle)


 * The Swept Volume per Operating Cycle is its Displacement. For a two-stroke engine, the operating cycle is one revolution; for a four-stroke, two revolutions.  Hence, Mean Effective Pressure in terms of Torque and engine parameters is
 * Mean Effective Pressure = 2 π (Torque) x (Revolutions per Cycle) / Displacement

Paradigm99 (talk) 10:07, 7 October 2008 (UTC)

Internal combustion engines also include gas turbines, which not having swept volumes don't have MEPs. MEPs also apply to any reciprocating engine, including steam engines which are external combustion. Would anyone disagree that the reference to IC engines in the first sentence should be changed to reciprocating engines? Will also check to see if there's any sources [likely to be quite old] that provide data on MEPs for steam engines that can be included in the table 82.47.136.229 (talk) 21:00, 5 November 2011 (UTC)

About the expression "specific torque"
The statement: "Notice that speed has dropped out of the equation and the only variables are the torque and displacement volume. Since the range of maximum brake mean effective pressures for good engine designs is well established, we now have an engine displacement independent measure of the torque producing capacity of an engine design (a specific torque of sorts). This is useful for comparing engines of different displacements." is unclear. Engine displacement, Vd, remains in both equations. Unless you mean that since we divide out the Vd then the bmep is Vd independant? How does having a range of bmep values help us get a T independent of Vd? I don't know the answers, I'm learning about this myself.Rgbutler (talk) 18:44, 16 February 2012 (UTC)
 * "Unless you mean that since we divide out the Vd then the bmep is Vd independant?" That is indeed what he means. The idea is that an engine's torque, for a particular engine design, will be directly proportional to the engine's displacement if we keep all the other parameters fixed. "Scaling up" the engine in displacement should correspondingly scale up its torque. But the scaling factor turns out to be proportional to BMEP, since all the other factors in the BMEP equation are constant (as long as we don't compare a four-stroke engine with a two-stroke one, which would change $$n_c$$). So in that sense, BMEP acts like a "specific torque", a torque per unit displacement. If we keep the displacement the same and increase the BMEP through other improvements to the engine (higher compression ratio, better breathing, forced induction, etc.), we should get an engine with more torque.
 * By the way, even though the article says BMEP is like a "specific torque", you can't get BMEP by simply dividing torque by displacement, because of how BMEP is defined. You need the factor of $$n_c {2 \pi}$$ to get the right BMEP value. Think of it this way: BMEP is defined as if the engine generated an entire cycle's worth of work by exerting that pressure on its piston over a single stroke of the piston (like a conventional steam engine would), whereas engine torque, which can be thought of as the equivalent force which would be applied to the crankshaft by a crank of unit length, is produced as the engine, during its full cycle, revolves over two full revolutions ($$4 \pi$$ radians) for a four-stroke engine or one full revolution ($$2 \pi$$ radians) for a two-stroke engine. --Colin Douglas Howell (talk) 01:12, 29 January 2018 (UTC)

$$n_\text{c} =2$$ for Wankel engines
this is wrong, as the Wankel engine takes 3 crankshaft revolution per unitary thermodynamic cycle.

From https://doi.org/10.4271/920309, let's disable injection and ignition for eleven faces of the total twelve. It's taking place only one 654.7 cm3 Otto cycle and the engine generates (ideally) 1/12 of torque and power. T = 50.7 N⋅m. N = 6500 min-1 = 108.3 s-1. P = 34.5 kW. I think we can agree on this.

pme = 2π ⋅ 3 ⋅ 50.7 N⋅m / 654.7 cm3 = 1.46 MPa

W = 1.46 MPa ⋅ 654.7 cm3 = 956 J

P = 956 J ⋅ 108.3 s-1 / 3 = 34.5 kW

Edoriel (talk) 09:19, 24 December 2023 (UTC) Edoriel (talk) 09:19, 24 December 2023 (UTC)


 * Hello Edoriel, I suppose youre trying to cite, as it gives some engine specs. If we assume that, as you have proposed, injection and ignition for eleven faces of the total twelve faces are disabled in a 5232 cm³ four-rotor Wankel engine, then the engine has an effective displacement of 436 cm³. Given p_me = 1.46 MPa, such an engine should produce 50.7 N·m of torque, and if the engine speed is 6500/min, then power should be 34.5 kW:



p_\text{me} = {2 \pi} {n_\text{c}} {T \over V_\text{d}} \rightarrow T = {{p_\text{me} V_\text{d}} \over {{2 \pi} {n_\text{c}}}} $$



1.46 \, MPa \cdot 436 \, cm^{3} \cdot (2 \pi 2)^{-1} \approx 50.7 \, N \cdot m $$



50.7 \, N \cdot m \cdot 6500 \, min^{-1} \cdot 2 \pi \cdot 60^{-1} \approx 34,500 \, W $$


 * Engine specs:


 * Formula for displacement and BMEP:


 * Your formula relies on a single-rotor engine with a chamber volume $$V_k = 654 \, cm^3$$, but you have used the BMEP formula that requires $$V_d$$. This is different from $$V_k$$. You can make this work if you use the two-stroke formula for deriving BMEP / torque instead of the four-stroke formula that's used in four-stroke engines, and that's what you have done:


 * Say we have a single-rotor Wankel engine with V_k=654 cm³, then V_d = 1308 cm³:



p_\text{me} = {2 \pi} {2} {152 \, N \cdot m \over 1308 \, cm^3} = 1.46 \, MPa $$


 * Then, with two faces disabled, V_d is now V_d/3, and T is also T/3:



p_\text{me} = {2 \pi} {2} {50.7 \, N \cdot m \over 436 \, cm^3} = 1.46 \, MPa $$


 * Summing this up, $$n_c = 2$$ for Wankel engines if $$V_d$$ is used. If you want to use $$V_k$$ (or $$V_k i$$ in an i-rotor engine), then you have to use $$n_c = 1$$ when calculating torque from BMEP or vice-versa. Don't get confused by $$V_d$$ and $$V_k i$$ as many (especially Japanese) works don't give any $$V_d$$ figures. Best regards, --Johannes (Talk) (Contribs) (Articles) 10:25, 24 December 2023 (UTC)
 * How can the "effective displacement" be 5232 cm³ / 12 = 436 cm³, if the face that operate the cycle displaces (by the engine geometry) Vk = 654 cm³? How can nc be 2 if (see the definition of this parameter) the shaft revolves 3 times to complete the cycle? My argument is that you are tweeking the value of nc to cope with the misguided evaluation of Vd.
 * This is thermodynamics applied to machines. The Otto cycle we are considering displaces 654 cm³ of working fluid, produces 956 J of work with 1.46 MPa of mean effective pressure. You can not tweek theese values.
 * P.S.: I've read (with fair enough google translation) Ansdale and Bensinger pages mentioned by you, in fact I'm here to argument against them.
 * Edoriel (talk) 11:21, 24 December 2023 (UTC)
 * "" – this is not what Wikipedia is for. Best regards, --Johannes (Talk) (Contribs) (Articles) 11:50, 24 December 2023 (UTC)
 * A source is as much reliable as correct its arguments are. Myopic mentions are just counterproductive.
 * Edoriel (talk) 12:12, 24 December 2023 (UTC)

Formulas modified on 2024-04-21
I think there are some problems with how you modified the formulas: Edoriel (talk) 08:02, 25 May 2024 (UTC)
 * The definition of $$p_{me}$$ (work of the cycle over displacement of the cycle) is missing, whereas all should start from it.
 * You use $$i$$ (number of cycles over one revolution), whereas $$n_{r}$$ (number of revolutions over one cycle) is more common.
 * You use $$M$$ for torque, whereas $$T$$ or $$\tau$$ are more common
 * In Note 1 you only cite Ansdale/Besinger interpretation. I think it would be fair to link to the Wankel engine article, so the reader can undertand all the three school of thoughts


 * Whatever is more common depends on whom you ask, but let's just see what Wikipedia says: "The symbol for torque is typically $$\boldsymbol\tau$$ (…). When being referred to as moment of force, it is commonly denoted by $M$." Apparently, for what I use it, $M$ is "commonly" used; $T$ seems to be not in use at all. Best, --Johannes (Talk) (Contribs) (Articles) 17:50, 25 May 2024 (UTC)