Efficiency Simulator

What Is the Efficiency Simulator?

How to use the efficiency formula physics simulator

1. Read the four cards before you touch anything. They sit above the sliders and they are already answering for a lamp: Stage 1 efficiency 75.00 %, Overall efficiency 75.00 %, Useful out 750.00 J and Wasted 250.00 J. The sub-line under the first spells the division out: the definition: 750 / 1000, and a ratio carries no unit.
2. Notice that the first two cards agree, and why. The compact grid underneath reads 1 of 4 next to Stages in play, below 100 %, and a chain of one stage is simply that stage. The grid also gives the same figure as a fraction, 0.7500, which is the form to carry onwards if you are going to multiply it.
3. Drag Useful output, of 1000 J in and watch three readings move together. At 880 the cards read 88.00 % and 120.00 J wasted; at 380 they read 38.00 % and 620.00 J. The slider stops at 1000, so you cannot ask for more out than went in.
4. Bring Stage 2 off 100 per cent and watch its own label change. It reads Stage 2 - not present until it moves, then Stage 2 efficiency. A second block appears in the flow lane with its own waste wedge, and the live count steps to 2 of 4.
5. Read the two efficiency cards against each other now. With the useful slider at 750 and stage 2 at 90 per cent, Stage 1 efficiency still reads 75.00 % while Overall efficiency has dropped to 67.50 %. Nothing about stage 1 changed; the chain behind it did.
6. Now look at the card the panel calls wrong. Average of the live stages - the WRONG answer reads 82.50 % at that setting. Add two more stages at 90 and it climbs to 85.00 % and then 86.25 %, while the overall figure falls to 60.75 % and then 54.68 %. The average rises as the answer falls.
7. Press Label it watts and check that nothing moves. Every percentage, the fraction, the live count and the average are byte-identical; only the unit symbol changes, so 295.34 J becomes 295.34 W. The button then reads Label it joules, because it names the unit the next press will switch to.
8. Press Reset when a chain has got away from you. It restores 750, 100, 100 and 100 and puts the unit label back to joules. Those are the lamp’s own values, so the lab always returns to a state with a known answer rather than to an arbitrary one.

Dragging is the right way to find out which readings a control is allowed to move, and a poor way to hit an exact figure — the useful slider steps a whole unit and the three stage sliders a whole percentage point. When you already have two measurements and want the division done on them, the efficiency calculator takes typed input in any unit and also declines the entries this lab cannot reach at all. The written guide to the efficiency formula in physics is where the method itself is set out, with the eight worked problems and the energy form against the power form.

One thing this panel will not decide for you is which of your two figures counts as useful, and that choice is upstream of every number on the screen. A lamp’s useful output is light and its heat is waste; swap the lamp for a heater and the same joules change sides. The guide to energy conversion examples is the page that asks that question and then hands the arithmetic over to this cluster, so it is the right place to settle the numerator before you start sliding.

Worked example: change one thing at a time

Nothing in the two tables below was worked out here. Each row is a setting the lab was put into through its own sliders and then read back from, cell by cell, so every string in them is the panel’s own. The first table moves one slider at a time; the second is the eight preset buttons in the order they appear.

One: build the four-stage chain one stage at a time

The useful slider stays at 380 in all four rows, so Stage 1 efficiency and Wasted at stage 1 never move. Only the three stage sliders change, one per row, and each one is a good stage.

Read the third column down and the last column down, and then compare them. The overall efficiency falls 38.00 %, 36.48 %, 33.56 %, 29.53 %. The average of the live stages rises 38.00 %, 67.00 %, 75.33 %, 78.50 %. Every stage added is a good one, and the two columns move in opposite directions.

That is the clearest thing this panel has to show, and it is why the average is printed at all. A chain is not improved by surrounding a bad stage with good ones. Each of the three stages takes its own cut of whatever reached it, so the waste column grows from 620.00 J to 704.66 J while Wasted at stage 1 sits unchanged at 620.00 J in every row.

The second column is the control in this experiment. 38.00 % in all four rows, because nothing about stage 1 was touched — which is also why the first card and the second card are kept separate rather than merged into one reading. The chain is a property of the whole lane, and stage 1 is a property of one slider.

Two: the eight presets, and what each one is for

These are the buttons above, with the full set of readings each one produces. The three boundary rows at the bottom are the ones worth sitting with, because each of them is a case a reader is likely to think the lab cannot handle.

Rows one and two are single stages and nothing more. 75.00 % and 88.00 % are what the useful slider was set to, not properties of any lamp or any kettle: every percentage in this lab is an arithmetic exercise with stated givens. Both rows read 1 of 4, and in both the average happens to be right, because a mean of one number is that number.

Rows three to five are the chain, and the last column is the point. 85.00 % against a real 72.00 %, 72.33 % against 31.28 %, 78.50 % against 29.53 %. The gap widens as the chain lengthens, which is exactly the opposite of what an average promises.

Row six is the only state where the lab draws no waste at all. An ideal lossless device reads 100.00 % with 0.00 J wasted, and the live count reads 0 of 4 with the words none live where a percentage would go. There is no average to take, so the panel says so rather than printing a figure it has not earned.

Row seven is a real device and it is answered, not refused. A useful output of 0 is a perfectly good setting: 0.00 % overall and the whole 1000.00 J wasted. The two boundaries bracket the whole lab, and every reachable setting sits between them, which is how you can tell that no slider combination here is undefined.

Row eight is the one that catches people out. Three stages are untouched and the fourth is at 50 per cent, so Stage 1 efficiency reads 100.00 %, Wasted at stage 1 reads 0.00 J and the chain still reads 50.00 %. Where in the chain the loss sits makes no difference to the product. The guide to what energy is in physics is where the joule the cards are counting in is set up.

Formula and symbol reference

The lab prints its own definitions in a fixed line under the drawing. Written out the same way: the efficiency of one stage is its useful output over its total input and carries no unit; multiplying that pure number by 100 gives a percentage; the waste is the input minus what arrives; and stages in series multiply, so eta_total = eta1 x eta2 x eta3 x eta4.

Nine rows follow and only four of them are something you drag. The rest are cards, cells of the compact grid, or quantities the panel names without giving you a control for — the fixed input is the clearest of those. For the sliders the last column gives the end stops and the step; for everything else it gives the strings the lab printed and the span it printed them over.

One row is worth reading before the table. The total input is fixed at 1000 and is not a control at all, which is what licenses every other figure on the screen to be read as a proportion. The same fixed figure is why a power and an energy are interchangeable here: a ratio of two powers measured over one interval is the ratio of the two energies, and the guide to power in physics is where those watts are worked out in the first place.

If you read one row twice, make it Average of the live stages. It is the only reading on the panel that is printed in order to be disbelieved, and the only one whose label contains the word wrong.

The physics of a chain, and why it can never beat its worst stage

The first claim the panel lets you test is that each stage divides what reached it rather than what started. That is why the flow lane tiles: block one begins at the left edge, every block after it begins where the one before it ended, and the gold survivor begins where the last waste block stopped. Multiply four fractions and you get the width of that survivor; nothing else in the drawing needs explaining.

The second claim follows from the first with no physics in it at all. Multiplying by a number below one can only make a result smaller, so a chain can never beat its worst stage and in practice falls below it. The fourth band draws exactly that comparison: the whole chain against what the worst stage alone would have left, on the same shared scale, with the chain the shorter of the two.

The third claim is the awkward one, and the panel is arranged around it rather than around the other two. An average is a sum, and efficiencies do not add. The compact grid prints the average anyway, labels it wrong, and lets you watch it climb while the real figure sinks — which is the one thing a static worked example cannot do.

None of this is the second law of thermodynamics, and the lab is careful not to borrow its authority. The ceiling here is energy conservation: the useful output is part of the input, and a part cannot exceed the whole. A heat engine does carry a further ceiling on top of this one, set by the temperatures it works between, and the Carnot efficiency guide is where that is computed — nothing on this page computes it.

Where the efficiency simulator breaks down

Every slider position this lab can reach is answered, and the arithmetic is not where it can let you down. The model behind it is, and so is the drawing. Nine limits sit under the readings on this page; three are choices the panel makes on purpose and six are bounds on what a panel of this shape can show at all.

There is no refusal to be reached here, and the lab does not pretend otherwise

The one entry this topic has to decline is a useful output larger than the total input, because that would be energy appearing from nowhere. You cannot set it: the useful slider stops exactly at the fixed 1000. So no state you can reach through these controls is undefined, and the refusal belongs to the efficiency calculator, where you type both figures yourself and it says why it will not answer. The guards are present in this lab too and were driven directly in testing; they simply have no reachable input.

The input is normalised, so the lab has no sense of scale

Everything here is measured against 1000 units, and that is what makes the widths honest as proportions. What it costs is any sense of size: a small motor and a large one at the same percentage lose quite different amounts of energy, and this panel draws the two identically because the input is pinned. Read the proportion here and take your own two measurements somewhere that will divide them.

A stage at 100 per cent is absent, not perfect, and that is a convention

With four slots and most chains shorter than four, the lab needs a way to say “this link is not in the circuit”, and 100 per cent is it. The slider relabels itself to Stage 4 - not present, nothing is drawn, and the live count excludes it. A real stage that genuinely measured 100 per cent would be indistinguishable from an absent one here, which is a limit of the convention rather than of the arithmetic.

The step grid is coarse, and some well-known figures are simply off it

The useful slider steps a whole unit out of 1000 and the three stage sliders a whole percentage point, so stage 1 moves in tenths of a percentage point and the other three in whole ones. 72.67 % is not on that grid, which is why the hoist from the written guide is not a preset here. Neither is a true two-thirds stage: the nearest setting prints 66.70 %, and chained with 85 per cent it gives 56.70 % rather than the 56.67 % a real two-thirds would. That gap is the subject of a section in the guide, not of this lab.

Four stages is the ceiling, and a longer chain needs two passes

There are four slots because the owner’s compact rule allows four sliders, not because chains stop at four. A six-stage chain has to be done as two groups and then multiplied, which is arithmetically identical because a product does not care how it is grouped, but the lab will not do it in one go. Multiply the fractions between passes rather than the percentages it printed.

No bar is a measurement, and no pixel count means anything

The scene is drawn to whatever width the canvas has, so the same chain occupies a different number of pixels on a phone and on a desktop. What is constant is the proportion: the full width always means the full input, and every block is a share of it. The exact figures live in the cards, the compact grid and the sentence strip, and those are what you should quote.

The caption bands shorten on a narrow screen, and a figure is dropped whole

Each band carries several wordings and picks the longest that fits, so the sentence under the drawing is shorter in a narrow column than on a wide screen. A ladder whose rungs carry numbers is dropped as a whole rung rather than shortened, because a partial figure is a different figure. Nothing you need is ever only in a band: every number in the scene is also in the panel.

A heat engine carries a second ceiling, and no slider here is aware of it

Perfect engineering still will not take a heat engine to 100 per cent, because the two temperatures it runs between impose their own limit underneath this general one. That limit is a separate calculation and nothing in this panel attempts it; the Carnot efficiency guide is where it is worked out. The figure above 100 per cent that a heat pump is sometimes quoted with is a different ratio again rather than a counterexample, and nothing here produces one either.

Two other quantities on this site are called efficiency and neither is this one

The ratio of two mechanical advantages is one of them: the mechanical advantage guide owns that quantity and the mechanical advantage lab draws it, and in that lab an efficiency is a slider you set rather than a figure you read. The temperature-driven ceiling is the other. Neither is computed in this lab and no figure for either is printed or implied anywhere on this page.

Where efficiency is actually used

Finding the one stage that is setting the scale

This is the everyday use and the panel is the fastest way to feel it. Set a chain, then walk each stage up and down in turn and watch which one moves the overall figure most. On the four-stage preset it is stage 1 at 38.00 %: improving it buys more than improving any of the other three, and the comparison band shows how much of the gap is the rest of the chain nibbling.

Deciding where an improvement is worth spending

Press the three-stage preset and try taking the 92 % stage to 100 per cent; then put it back and take the 40 % stage up instead. The second move is worth several times the first, and the reason is in the product rather than in any one stage. A chain that reads 31.28 % against a worst stage of 40.00 % has told you where to look before you have costed anything.

Turning a percentage into a figure somebody will act on

The Wasted card is the one that becomes money, heat or a cooling requirement. 29.53 % is hard to argue with and easy to ignore; 704.66 J of every 1000 J going somewhere other than where you wanted is not. Quote the waste and keep the percentage as the supporting figure rather than the headline.

Unlearning the average, before an exam rather than during one

The habit of averaging stage efficiencies is extremely hard to shift by being told. Set two stages at 80 and 90 per cent, read 85.00 % on a card that calls itself wrong and 72.00 % on the one that is right, then lengthen the chain and watch the two diverge. Three minutes of that does more than a paragraph, which is the reason the reading exists.

Checking that a quoted overall figure agrees with its own stages

If somebody hands you both a stage list and an overall figure, the two have to be consistent. Type the stages into the sliders and compare: a quoted overall figure above the product is impossible, and one far below it means a stage is missing from the list you were given. The lab will not tell you which, but it will tell you that the two numbers cannot both be right.

Showing that the unit genuinely does not matter

A ratio of two quantities of the same kind is unit-free, and the button is the proof rather than the claim. Press it and every figure stays where it is while J becomes W. If you want to see where those watts came from in the first place, the power simulator and the work and power calculator are the two halves of that step.

Where to go next

A panel can show you which readings a control is allowed to move, and that is the end of what a panel is for. Efficiency in physics is where the subject itself is written out: the definition, the two forms of the formula, which figure counts as useful, the chain, and eight worked problems with every step shown. The calculator that takes typed figures heads the related tools below.

Two posts sit either side of this one on the same question. The energy conversion examples guide is the page that reserved this topic and handed it over, and the conservation of energy guide is where the ceiling this lab never exceeds actually comes from.

Three more guides own the quantities this lab deliberately leaves alone. The mechanical advantage guide and the Carnot efficiency guide have the two other ratios that are also called efficiency, and the guide to power in physics is where the watts come from. The guide to work done in physics and the specific heat capacity guide supply the two measurements most kettle and hoist problems start from.

Beyond those there is the simulation library, an index of calculators, and the blog for everything written out at length.