Need Help Designing an Experiment
I want to do an A-B comparison between two sauce pans. The experiment is to see which pan heats up a a batch of water faster.
Problem: the two sace pans are not the same size. Nor are they the same shape. But they are not that different.
Background: I want to test one of my Cuisinart multi-clad pots against a friend's All-Clad Copper Core. I've always been curious about the copper core and whether it is actualy more responsive than other types of S/S cookware. I was only able to borrow my friend's 2 qt copper core sauce pan for a limited time. The closest similar size in my MultiClad line is a 1.5 qt. (next size up that I have is a 2- 3/4 qt). The 2 qt All-Clad is a little taller and narrower than the 1.5 qt multi-clad.
I ran a few preliminary tests using the same volume of water (of the same temperature) in each pot on the same stove top burner (electric). The copper core brought the water to a rolling boil about a minute faster than the multi-clad. Just out of curiosity, I ran the same test in the larger multi-clad 2 3/4 qt size pot. This resulted in an even faster time than the copper core, which didn't make sense. There must be something about heating a larger pot with the same volume of water that heats the liquid faster. I thought maybe it's the height of the water relative to the bottom of the pan. So I went back to testing the 1.5 qt multi-clad against the 2 qt All-Clad copper core with the same level of water in each (2"). This time, the 1.5 qt was faster. But now I don't know what I've learned.
I need help designing an experiment that can simulate a direct A-B comparison between the two different size pots. Should the water be the same volume? Or the same level? Or should the water fill the same relative volume of each pot? Or is this whole experiement invalid without the same size pots?
What's the best way to eliminate variables and make the fairest comparison?
The problem is that it is difficult to compare two cookware of different sizes and shapes. Yes, you can get some results out of the experiment, but it will be difficult to give any meaning to it.
"I ran the same test in the larger multi-clad 2 3/4 qt size pot. This resulted in an even faster time than the copper core, which didn't make sense"
This is probably because the larger pot has (1) either a larger base, and therefore captures/absorbs more heat from the stove, or (2) a taller side, and therefore preserves more heat.
"Should the water be the same volume? Or the same level? Or should the water fill the same relative volume of each pot? Or is this whole experiement invalid without the same size pots?"
It all depends what is your question. All experiments start with a question in which you want to answer. If you want to answer the question: "which cookware has the greater heat transfer to the food, then you should use the same amount of water.
The fact that your two sauce pans are different capacity, I believe, introduces a variable that you have no way to normalize. Thus I believe you will never be able to set up conditions where you can make a fair comparison of which pan heats faster. I don't know the particulars of these two pieces of cookware, but typically a 1.5 qt pan will have both different diameter and height than a 2 qt pan, the same with the 2&3/4 pan. That different surface area on an electric hob will in itself change the way the pan heats. Water heats via the method of mixtures, that is, the water in contact with the hot part of the pan mixes with the water not in contact with the hot part of the pan, so the area of the bottom of the pan matters and the volume of water that needs to be heated matters. If you put 1 qt. of water in two pans of different sizes the one with the most surface area will boil first assuming they are both made of materials suitable for the task. In other words, if the two are similar enough the surface area will mask any difference in material performance.
The other big thing that you have to take into account is the thermal mass of the pan and the thickness of the bottom. A thicker pan may take longer to boil water because of the time it takes to heat the bottom, even if it has better heat transfer. Since boiling water doesn't take into account a very important factor in cooking, even heat distribution, a pan with low thermal mass will likely boil water quicker but not have even heat across the bottom that is necessary not to burn sauces. My guess is if you went out and bought the cheapest, thinest, 2 qt sauce pan you could find that was aluminum, no SS, it would boil water faster than either of the pans you are evaluating. That doesn't make it a better sauce pan.
The only way I know to make the fairest comparison is to use two pans that are as identical in size and shape as you can possibly find. And that will just be for those two pans and will not be applicable to other brands and shapes with different construction or thickness.
To follow up Mike's point. Technically speaking, you can set up to test which pan heats up the content faster. The real challenge is to get some bigger meaning out of it. In other words, pan A heats up water faster than pan B does, but it does not imply pan A has a more efficient design.
Mike is correct in term of the thin light cookware statement. Thermal capacity is definitely one reason. There is another reason as well. The heat transfer itself is greater with a thinner bottom (thus shorter distance). Thereis a balance to be made between heat response and temperature evenness, and there isn't a magic number to this. For a given design, you gain one, by losing the other one.
One more thing to consider for stainless steel cladded cookware. Stainless steel significantly affects the overall heat response by providing a high thermal resistivity. So, in many ways, the pan with the thinnest stainless steel walls will response to external heat the fastest. Yet, the cookware with the thinnest stainless steel is also the less robust and less durable.
At the end, every one will have slightly different critera. What is good for you may not be good for another. As long as your pan/pot is working fine for your style, then it is a good pan.
Having done a number of these experiments myself, I can tell you that it's all about doing your best to equalize all other variables. Unfortunately for you (and us, deprived of your results), pan size/surface area is one of the larger variables. If you don't have equally sized pans to compare, it is difficult.
Do you only have these 3 pans to compare? What are your results when you time boils with all the pans, say, 3/4 full? Starting from a different conceptual starting point, assuming in advance that the A-C and multiclad will perform identically, and if you have equalized other variables like hob size, you should see some linear relationship in the results. It follows that if you *don't* see something resembling linearity, you *may* be seeing a real difference that *may* be attributable to the construction difference. The problem with this approach is that it relies on inductive logic and in your case a tiny sample. If you had 4 pans of each line and the sizes overlapped (e.g., A-C in 3,5,7 & 9", and multi in 4,6,8 & 10"), you would have a larger sample, more data, and perhaps more reason for confidence in the conclusion you arrive at.
Still, if I read your OP correctly, I think I can make a couple of generalizations. It sounds as if your friend's A-C 2Q pan's footprint is smaller than your multiclad 1.5Q's. Correct? The fact that a smaller-footprint pan boiled a given volume of water faster (and by a minute) than did a wider-footprint pan I find to be significant. If your hob output was constant over the entire surface area, that result means that the A-C beat the multi by a minute and with *less* energy dumped into the A-C pan and its water. (This is no giant energy savings because the unoccupied area of the coil was still dumping energy into the room). I think it is a fair conclusion to extrapolate that an A-C with a surface area identical to your multi 1.5Q would boil the same amount of water *more* than a minute faster.
You might try this: Calculate the pans' bottom surface area in contact with the coil. Then adjust your volume of water so that you have the same volume to surface area ratio. This would be a fairer test. But be prepared for the A-C's margin of victory to be even greater.
Hope This Helps,
I think the experiment with 2" of water in each pan was probably fairly close to what you suggest in the last paragraph. But in the experiment, the multiply pan was faster. Honestly, I think there are too many variables in the experiment to get accurate results.
Seitan, to get any level of accuracy, for starters you need to repeat the experiment a minimum of 5 times and preferably 10 times to get values with some level of reliability and they need to be timed as precisely as possible. Then you need to run the statistics to get the mean and standard deviation of your test. This data can then be ploted with error bars to determine if there are stastical differences in the numbers. You also need an accurate thermometer and bring the water to some temperature that is fixed, not a rolling boil which is somewhat subjective. You will need a procedure for testing the electric coils for start temperature and final temperature to insure the difference isn't in the coil and not the pan. Also important is where the pan is placed on the coil, so that each pan recieves the same contact area (within the limits of pan size) and same heat gradient across the coil every time, otherwise the standard deviation will be greater and void the experiment. This only leaves two variables, the one you want to test and the one that you are forced into with the availability of pans. That's a tough one and I don't know exactly how you are going to eliminate or compensate for that variable. Perhaps Kaleo's suggestion for a volume adjusted by the surface area of the bottom of the pan is as close as you are going to get, but even that may vary considerably with differing radii for the two pans where the bottom and sides meet. I know that looks like a lot of work, but if you want results that will stand up to review, then that's what it's going to take. We do a burn test and to insure reliability we use gas from a cylinder that has a specific burn temperature and we measure the flame height from the end of the burner, this is just the level of accuracy that is needed to conduct an experiment.
I'm still going to guess that the thinnest pan wins the boiling water test. It's the shortest distance from the heat source to the water and the water doesn't care about hot spots.
Very helpful suggestions. Thanks.
I see I'm going to have to cut down the margin of error even more. I'll use a thermometer instead of eyeballing a rolling boil. I'll use a larger sample size as well. Incidently, both pans cover the small electric hob. The A-C is about half an inch narrower than the M-C, but about an inch or so taller.
I'm also guessing that the smaller the pot, the less differences can be picked out from the margin of error. Bigger pots might yield more noticeable results from the tests.
I'll report back with updated results.
You might also want to note how much each pan weighs. Put them on a food scale.
Use a measuring cup to measure the water volume not the height in the pan. Keep the volume of water a constant. But use more water, like 1 quart (4 cups) so you'll see a bigger difference.
Use the small electric hob and keep pan centered so the surface contact area is a constant. Use the SAME electric hob.
I think this experiment is very interesting. I have a hypothesis which may guide your experiments: the heavier pot with more heat capacity will boil in the shortest amount of time.
"What's the best way to eliminate variables and make the fairest comparison?"
You have variables all over the place. I don't see how you can eliminate them or even control them unless you are fabricating the pots yourself. The best you can do is to try to understand them. A big variable is the heat capacity of the pots themselves. That depends on the materials and the mass of each. The pot will soak up energy as it heats up. The more energy it can contain, the longer it will take to reach a given temperature.
I was thinking that as well. On the other hand, there is a way to relatively minimize this by increase the volume of water. This will relatively reduce the heat capacity contribution to the total heat capacity. In other word, a 8 cups of water will tell a better story than a tablespoon of water. That being said, Seitan will need to form a null hypothesis in the first place; colloquial as a testing question. One design an experiment around a null hypothesis, not the other way around.