The Temperature Stall

[nathanm]

Here is the graph showing BBQ stall is due to wet-bulb temperature effects (humidity). Chris Young, one of my co-authors on the Modernist Cuisine book ran these experiments last night and this morning.

We took one brisket, cut it in two. One was sous vide cooked, the other was not covered. Both were put on a wire rack in a Rational combi-oven in convection mode at 90C/194F, with a temperature sensor in the center (core).

The wet-bulb temperature comes from an home-made wet bulb sensor (details of the sensor, and this whole topic are given in my upcoming book).

Dry bulb temperature is from a sensor in the oven. You will notice that the sous vide sample actually is higher than the oven temperature. How can that be? The reason is that the oven temperature varies at various places in the oven by a few degrees.

The sous vide brisket makes a smooth transition from its initial temperature up to 90C/194F, reaching that point in about 10,000 seconds (2.78 hours). There is NO STALL in the sous vide sample.

The glitch in the dry bulb and wet bulb temperatures near the start is caused by opening the oven to put the meat in.

The wet bulb temperature starts out at about 60C/140F. The WB temp rises as evaporation from the meat makes the oven higher humidity. It reaches a peak of about 80C, then declines over time becaues the meat is drying out, and the oven is venting air and moisture.

The non-bagged brisket (labeled traditional) has a stall between about 7500 seconds and 15000 seconds (between 2 hours and 4 hours after the start). Eventually the surface of the meat dries out, so that the the surface reaches dry bulb temperature - at that point the stall ends and the meat temperature rises again.

I think this pretty conclusively shows why there is a stall.

The actual temperature of the stall will depend on the humidity in the oven, and a couple other factors.

[PedroG]

Here is the graph showing BBQ stall is due to wet-bulb temperature effects (humidity)..... snip snip snip

I think this pretty conclusively shows why there is a stall.

The actual temperature of the stall will depend on the humidity in the oven, and a couple other factors.

Thanks, Nathan!

This is very illustrative. I think with your and Douglas' post everything has been said.

BTW a Rational 61 SCC (7336 EUR) seems to be out of the reach of a home cook, but its temperature stability within 1°C is impressive.

[infernooo]

nathanm: I posted your findings and theories on one of the big smoking forums (http://www.bbq-brethren.com/forum/showthread.php?t=90123), and one of the replies was this:

From what I can tell wet bulb and dry bulb temperature phenomenon has to do with air temperature and the relative humidity and rise of temperature of the air. This process seems to be used in the food industry in the dehydration of foods like making dried potatoes and such air dried food items that have to really dry. Even after a brisket is injected with more liquid the wet bulb effect is not sustained for a longer time. The science of collagen breakdown has been studied extensively by the meat industry and if anyone cared to pay for the research articles available we might get a more clear picture. WB DB may however play a role in some situations but the collagen stall is real. .

Wet bulb/dry bulb is only germaine if the discussion is about gas. It has no meaning in a discussion of liquid/solid temperature measurements. It is good information about stack conditions as moist air can carry more energy (specific heat) which means that food will cook quicker.

This has been a learning experience and I appreciate your insight. Now- one more question. How does the location of the fire affect this (convection vs Radiant) heat?

Seems like the radiant energy would penetrate the meat better but what effect would that have on the colagens?

According to this article there seems to be an error in the way these guys measured the temperature of the surface of the meat which they state is the wet bulb temp. Wouldn't this cause a discrepancy in their outcomes?

http://onlinelibrary.wiley.com/doi/10.1111/j.1365-2621.1976.tb14386.x/abstract

It also seems to me that when cooking Sous Vide or in a pressure cooker, there are other effects at work that would change the dynamics of cooking that they fail to discuss or take into consideration at all. Comparing a wood fired, free draft smoker to an electric/gas Convection oven and on top of that one product is in a Vacuum sous Vide bath? It seems wrong to compare the two cooking methods and then draw conclusions that way. Apples and oranges it seems to me.... I'm not trying to defend the Phase Change theory at all, as I really don't care what ends up causing the stall as long as I can get to the bottom of it. I just can't find any reference that leads to their conclusions at all. Wet Bulb Dry Bulb temps seem to be relevant to gas atmospheres and those that rely on them for drying and dehydrating to maintain a level of safety from bacteria growth.

Any thoughts?

[Paul Kierstead]

WB DB may however play a role in some situations but the collagen stall is real.

I got nathan who has done experiments, published the data and has a solid theory behind it (which is confirmed by the experiments). OTOH, I got some random guy who makes an assertion with no data and no theory other then referencing articles he hasn't read and we would have to pay to read.

I think I'll lean to the wet-bulb theory; it could be wrong, but it seems much more likely to be right.

[nathanm]

nathanm: I posted your findings and theories on one of the big smoking forums (http://www.bbq-brethren.com/forum/showthread.php?t=90123), and one of the replies was this:

From what I can tell wet bulb and dry bulb temperature phenomenon has to do with air temperature and the relative humidity and rise of temperature of the air. This process seems to be used in the food industry in the dehydration of foods like making dried potatoes and such air dried food items that have to really dry. Even after a brisket is injected with more liquid the wet bulb effect is not sustained for a longer time. The science of collagen breakdown has been studied extensively by the meat industry and if anyone cared to pay for the research articles available we might get a more clear picture. WB DB may however play a role in some situations but the collagen stall is real. .

Wet bulb/dry bulb is only germaine if the discussion is about gas. It has no meaning in a discussion of liquid/solid temperature measurements. It is good information about stack conditions as moist air can carry more energy (specific heat) which means that food will cook quicker.

This has been a learning experience and I appreciate your insight. Now- one more question. How does the location of the fire affect this (convection vs Radiant) heat?

Seems like the radiant energy would penetrate the meat better but what effect would that have on the colagens?

According to this article there seems to be an error in the way these guys measured the temperature of the surface of the meat which they state is the wet bulb temp. Wouldn't this cause a discrepancy in their outcomes?

http://onlinelibrary.wiley.com/doi/10.1111/j.1365-2621.1976.tb14386.x/abstract

It also seems to me that when cooking Sous Vide or in a pressure cooker, there are other effects at work that would change the dynamics of cooking that they fail to discuss or take into consideration at all. Comparing a wood fired, free draft smoker to an electric/gas Convection oven and on top of that one product is in a Vacuum sous Vide bath? It seems wrong to compare the two cooking methods and then draw conclusions that way. Apples and oranges it seems to me.... I'm not trying to defend the Phase Change theory at all, as I really don't care what ends up causing the stall as long as I can get to the bottom of it. I just can't find any reference that leads to their conclusions at all. Wet Bulb Dry Bulb temps seem to be relevant to gas atmospheres and those that rely on them for drying and dehydrating to maintain a level of safety from bacteria growth.

Any thoughts?

There are several misconceptions in this text passage. Feel free to pass this along.

Meat is mostly water! There was a classic Star Trek epiosode where an alien species refers to humans as "ugly bags of mostly water" and that pretty much sums up what any animal is (well, the ugly part can be debated). So no matter whether you inject or brine or just use meat as-is, there is plenty of water in the meat to evaporate. In the case of brisket it is about 71% water.

The method of heating the meat does not matter, the same effect occurs for both radiative and convective heating.

Now, as it so happens, radiant heating plays essentially no role in most barbeque, because radiant heating is only important when there is a high temperature source. Most barbeque is smoked with an air temperature (dry bulb) of 90C/194F to 110C/230F. At those tempertaures radiant heating is insignificant. Most barbeque rigs / smokers have the fire baffled so the meat does not directly recieve IR radiation from it.

South American asado (from Chile or Argentina especially) does use radiant heat, but that is a very different method.

However, even if there was radiant heating, it wouldn't matter. The point about wet bulb temperature is that evaporating water takes energy, so a wet surface that is evaporating will be cooler than a dry surface. It doesn't matter how you heat it, if the surface is wet, then it will be cooler than a dry surface if water can evaporate.

When he says that wet bulb / dry bulb is about gas, I think there is some confusion. Wet bulb temperature is the temperature of a wet surface which is cooled by evaporation. It is a surface temperature. The air temperature is the dry bulb temperature. The reason that "gas" (i.e. air) is involved is that in order for the water to evaporate it must go into the air. If the air is already "full" of water (meaning that relative humidity is 100%) then evaporation can't occur.

Anybody who sweats knows this - sweating is done to take advantage of evaporative cooling. The reason that we feel more uncomfortable in high humidity is that our sweating doesn't work as well.

I am not sure that he understands that the temperature tests I did were not in a water bath. I took a vacuum sealed brisket and cooked it next to an uncovered brisket, but they were in the same oven. The sous vide bag simply stopped the evaporation.

There is a TINY effect due to collagen, but it is so tiny that it does not show up unless you use a differential scanning calorimeter. If there was a large collagen effect, then we would see it in the temperature profile for the sealed brisket with no evaporation. But we don't.

The test I did was in a convection oven, but a "free draft wood smoker" will not change anything. Water still evaporates! The existence of some smoke in the air won't stop water from evaporating. The smoke build up on the surface of the brisket may hinder evaporation slightly. The free draft part means that the smoker would, if anything, have a lower humidity than in the convection oven because the convection oven recirculates air to some degree while the smoker may, or may not depending on how open the dampers are.

The amout of draft in the smoker, the way air circulates, how full the smoker is, the dry bulb temperature in the smoker, the relative humidity of the air outside the smoker will all make small differences. That is why different people report a "stall" of different temperatures and durations.

The humidity outside the smoker has some effect, but only a small effect. The hotter air is, the more water it will hold. If you take air and heat it up to 90C/194F to 110C/230F, it will be very low relative humidity, no matter how moist the air outside is.

Finally, he can find no reference supporting what I am saying here because, as far as I know, nobody has explained the BBQ "stall" this way before. It is a new explanation. I suspect that some food scientist somewhere may well have figured this out, but I am not aware of any. But that doesn't mean it is wrong - it just means it is new.

The paper he quotes from Journal of Food Science supports ALL of what I am saying, by the way. It is a good early article on the topic of roasting meat. It confirms that there is substantial evaporative losses, and it confirms that the meat cooks with the surface at the wet bulb temperature.

Edited August 23, 2010 by nathanm (log)

[infernooo]

Hi Nathan,

I just wanted to shoot you a quick thank you for the extensive replies thus far on the "stalling" of internal temperatures of meat, it has been extremely interesting to read and I appreciate the time you have taken to experiment and explain!

[PedroG]

nathanm: I posted your findings and theories on one of the big smoking forums (http://www.bbq-brethren.com/forum/showthread.php?t=90123), and one of the replies was this:

From what I can tell wet bulb and dry bulb temperature phenomenon has to do with air temperature and the relative humidity and rise of temperature of the air. This process seems to be used in the food industry in the dehydration of foods like making dried potatoes and such air dried food items that have to really dry. Even after a brisket is injected with more liquid the wet bulb effect is not sustained for a longer time. The science of collagen breakdown has been studied extensively by the meat industry and if anyone cared to pay for the research articles available we might get a more clear picture. WB DB may however play a role in some situations but the collagen stall is real. .

Wet bulb/dry bulb is only germaine if the discussion is about gas. It has no meaning in a discussion of liquid/solid temperature measurements. It is good information about stack conditions as moist air can carry more energy (specific heat) which means that food will cook quicker.

This has been a learning experience and I appreciate your insight. Now- one more question. How does the location of the fire affect this (convection vs Radiant) heat?

Seems like the radiant energy would penetrate the meat better but what effect would that have on the colagens?

According to this article there seems to be an error in the way these guys measured the temperature of the surface of the meat which they state is the wet bulb temp. Wouldn't this cause a discrepancy in their outcomes?

http://onlinelibrary.wiley.com/doi/10.1111/j.1365-2621.1976.tb14386.x/abstract

It also seems to me that when cooking Sous Vide or in a pressure cooker, there are other effects at work that would change the dynamics of cooking that they fail to discuss or take into consideration at all. Comparing a wood fired, free draft smoker to an electric/gas Convection oven and on top of that one product is in a Vacuum sous Vide bath? It seems wrong to compare the two cooking methods and then draw conclusions that way. Apples and oranges it seems to me.... I'm not trying to defend the Phase Change theory at all, as I really don't care what ends up causing the stall as long as I can get to the bottom of it. I just can't find any reference that leads to their conclusions at all. Wet Bulb Dry Bulb temps seem to be relevant to gas atmospheres and those that rely on them for drying and dehydrating to maintain a level of safety from bacteria growth.

Any thoughts?

There are several misconceptions in this text passage. Feel free to pass this along.

Meat is mostly water! There was a classic Star Trek epiosode where an alien species refers to humans as "ugly bags of mostly water" and that pretty much sums up what any animal is (well, the ugly part can be debated). So no matter whether you inject or brine or just use meat as-is, there is plenty of water in the meat to evaporate. In the case of brisket it is about 71% water.

The method of heating the meat does not matter, the same effect occurs for both radiative and convective heating.

Now, as it so happens, radiant heating plays essentially no role in most barbeque, because radiant heating is only important when there is a high temperature source. Most barbeque is smoked with an air temperature (dry bulb) of 90C/194F to 110C/230F. At those tempertaures radiant heating is insignificant. Most barbeque rigs / smokers have the fire baffled so the meat does not directly recieve IR radiation from it.

South American asado (from Chile or Argentina especially) does use radiant heat, but that is a very different method.

However, even if there was radiant heating, it wouldn't matter. The point about wet bulb temperature is that evaporating water takes energy, so a wet surface that is evaporating will be cooler than a dry surface. It doesn't matter how you heat it, if the surface is wet, then it will be cooler than a dry surface if water can evaporate.

When he says that wet bulb / dry bulb is about gas, I think there is some confusion. Wet bulb temperature is the temperature of a wet surface which is cooled by evaporation. It is a surface temperature. The air temperature is the dry bulb temperature. The reason that "gas" (i.e. air) is involved is that in order for the water to evaporate it must go into the air. If the air is already "full" of water (meaning that relative humidity is 100%) then evaporation can't occur.

Anybody who sweats knows this - sweating is done to take advantage of evaporative cooling. The reason that we feel more uncomfortable in high humidity is that our sweating doesn't work as well.

I am not sure that he understands that the temperature tests I did were not in a water bath. I took a vacuum sealed brisket and cooked it next to an uncovered brisket, but they were in the same oven. The sous vide bag simply stopped the evaporation.

There is a TINY effect due to collagen, but it is so tiny that it does not show up unless you use a differential scanning calorimeter. If there was a large collagen effect, then we would see it in the temperature profile for the sealed brisket with no evaporation. But we don't.

The test I did was in a convection oven, but a "free draft wood smoker" will not change anything. Water still evaporates! The existence of some smoke in the air won't stop water from evaporating. The smoke build up on the surface of the brisket may hinder evaporation slightly. The free draft part means that the smoker would, if anything, have a lower humidity than in the convection oven because the convection oven recirculates air to some degree while the smoker may, or may not depending on how open the dampers are.

The amout of draft in the smoker, the way air circulates, how full the smoker is, the dry bulb temperature in the smoker, the relative humidity of the air outside the smoker will all make small differences. That is why different people report a "stall" of different temperatures and durations.

The humidity outside the smoker has some effect, but only a small effect. The hotter air is, the more water it will hold. If you take air and heat it up to 90C/194F to 110C/230F, it will be very low relative humidity, no matter how moist the air outside is.

Finally, he can find no reference supporting what I am saying here because, as far as I know, nobody has explained the BBQ "stall" this way before. It is a new explanation. I suspect that some food scientist somewhere may well have figured this out, but I am not aware of any. But that doesn't mean it is wrong - it just means it is new.

The paper he quotes from Journal of Food Science supports ALL of what I am saying, by the way. It is a good early article on the topic of roasting meat. It confirms that there is substantial evaporative losses, and it confirms that the meat cooks with the surface at the wet bulb temperature.

I totally agree. The BBQ brother should be invited to repeat Nathan's experiment in his BBQ smoker with two cuts of brisket, one naked and the other wrapped in cling film to avoid evaporation (vacuum-sealing is not necessary). To try to visualize the collagen-melting-stall he might use a bunch of beef achilles tendons glued together with transglutaminase, wrapped in cling film to rule out evaporation cooling.

[IndyRob]

This matter appears to be well settled, but I just ran across what appears to be an independent confirmation using slightly different methods. So, just place this in the record....

http://www.huffingtonpost.com/craig-goldwyn/physicist-cracks-bbq-mystery_b_987719.html

[Ashen]

Thanks to all who contributed , this is very interesting info on this topic.

I don't think it will change the way I do brisket though. I have used both the traditional method , in a charcoal water smoker with wet mop ,and then also using a "texas crutch" midway into the cook.(foil wrapping). There is a noticable difference between the two imo at the end of the cooks, and the traditional method just produces the kind of product I want for brisket. I have basically switch over to the foil wrap option for pork shoulder though, I pull the foil off near the end and let the bark dry . It cuts the cook time way down and I find I like the finished product better this way.

[Neekerbocker]

nathanm: I posted your findings and theories on one of the big smoking forums (http://www.bbq-breth...ead.php?t=90123), and one of the replies was this:

From what I can tell wet bulb and dry bulb temperature phenomenon has to do with air temperature and the relative humidity and rise of temperature of the air. This process seems to be used in the food industry in the dehydration of foods like making dried potatoes and such air dried food items that have to really dry. Even after a brisket is injected with more liquid the wet bulb effect is not sustained for a longer time. The science of collagen breakdown has been studied extensively by the meat industry and if anyone cared to pay for the research articles available we might get a more clear picture. WB DB may however play a role in some situations but the collagen stall is real. .

Wet bulb/dry bulb is only germaine if the discussion is about gas. It has no meaning in a discussion of liquid/solid temperature measurements. It is good information about stack conditions as moist air can carry more energy (specific heat) which means that food will cook quicker.

This has been a learning experience and I appreciate your insight. Now- one more question. How does the location of the fire affect this (convection vs Radiant) heat?

Seems like the radiant energy would penetrate the meat better but what effect would that have on the colagens?

According to this article there seems to be an error in the way these guys measured the temperature of the surface of the meat which they state is the wet bulb temp. Wouldn't this cause a discrepancy in their outcomes?

http://onlinelibrary...4386.x/abstract

It also seems to me that when cooking Sous Vide or in a pressure cooker, there are other effects at work that would change the dynamics of cooking that they fail to discuss or take into consideration at all. Comparing a wood fired, free draft smoker to an electric/gas Convection oven and on top of that one product is in a Vacuum sous Vide bath? It seems wrong to compare the two cooking methods and then draw conclusions that way. Apples and oranges it seems to me.... I'm not trying to defend the Phase Change theory at all, as I really don't care what ends up causing the stall as long as I can get to the bottom of it. I just can't find any reference that leads to their conclusions at all. Wet Bulb Dry Bulb temps seem to be relevant to gas atmospheres and those that rely on them for drying and dehydrating to maintain a level of safety from bacteria growth.

Any thoughts?

There are several misconceptions in this text passage. Feel free to pass this along.

Meat is mostly water! There was a classic Star Trek epiosode where an alien species refers to humans as "ugly bags of mostly water" and that pretty much sums up what any animal is (well, the ugly part can be debated). So no matter whether you inject or brine or just use meat as-is, there is plenty of water in the meat to evaporate. In the case of brisket it is about 71% water.

The method of heating the meat does not matter, the same effect occurs for both radiative and convective heating.

Now, as it so happens, radiant heating plays essentially no role in most barbeque, because radiant heating is only important when there is a high temperature source. Most barbeque is smoked with an air temperature (dry bulb) of 90C/194F to 110C/230F. At those tempertaures radiant heating is insignificant. Most barbeque rigs / smokers have the fire baffled so the meat does not directly recieve IR radiation from it.

South American asado (from Chile or Argentina especially) does use radiant heat, but that is a very different method.

However, even if there was radiant heating, it wouldn't matter. The point about wet bulb temperature is that evaporating water takes energy, so a wet surface that is evaporating will be cooler than a dry surface. It doesn't matter how you heat it, if the surface is wet, then it will be cooler than a dry surface if water can evaporate.

When he says that wet bulb / dry bulb is about gas, I think there is some confusion. Wet bulb temperature is the temperature of a wet surface which is cooled by evaporation. It is a surface temperature. The air temperature is the dry bulb temperature. The reason that "gas" (i.e. air) is involved is that in order for the water to evaporate it must go into the air. If the air is already "full" of water (meaning that relative humidity is 100%) then evaporation can't occur.

Anybody who sweats knows this - sweating is done to take advantage of evaporative cooling. The reason that we feel more uncomfortable in high humidity is that our sweating doesn't work as well.

I am not sure that he understands that the temperature tests I did were not in a water bath. I took a vacuum sealed brisket and cooked it next to an uncovered brisket, but they were in the same oven. The sous vide bag simply stopped the evaporation.

There is a TINY effect due to collagen, but it is so tiny that it does not show up unless you use a differential scanning calorimeter. If there was a large collagen effect, then we would see it in the temperature profile for the sealed brisket with no evaporation. But we don't.

The test I did was in a convection oven, but a "free draft wood smoker" will not change anything. Water still evaporates! The existence of some smoke in the air won't stop water from evaporating. The smoke build up on the surface of the brisket may hinder evaporation slightly. The free draft part means that the smoker would, if anything, have a lower humidity than in the convection oven because the convection oven recirculates air to some degree while the smoker may, or may not depending on how open the dampers are.

The amout of draft in the smoker, the way air circulates, how full the smoker is, the dry bulb temperature in the smoker, the relative humidity of the air outside the smoker will all make small differences. That is why different people report a "stall" of different temperatures and durations.

The humidity outside the smoker has some effect, but only a small effect. The hotter air is, the more water it will hold. If you take air and heat it up to 90C/194F to 110C/230F, it will be very low relative humidity, no matter how moist the air outside is.

Finally, he can find no reference supporting what I am saying here because, as far as I know, nobody has explained the BBQ "stall" this way before. It is a new explanation. I suspect that some food scientist somewhere may well have figured this out, but I am not aware of any. But that doesn't mean it is wrong - it just means it is new.

The paper he quotes from Journal of Food Science supports ALL of what I am saying, by the way. It is a good early article on the topic of roasting meat. It confirms that there is substantial evaporative losses, and it confirms that the meat cooks with the surface at the wet bulb temperature.

Thank you very much Nathan for your information, it is very informative. I've been trying to put this information to use, what are your thoughts with regards to the following?

I've been trying to figure out the best method to control temperature and humidity in my Bradley smoker. For pulled pork, I usually had a large shallow water pan in the smoker and smoke/cook for 18 hours total at low temperatures (190F), but it seems increasingly clear that a combination of smoking and sous vide cooking will give me better results.

This is what I've done so far: I've brined 16 lbs of pork shoulder (2 pieces) for 24 hours in a weak salt and paprika solution, followed by a spice rub. My Bradley smoker is in my shed and has a chimney to vent outside (so I can smoke in rain and winter) and is controlled using an Auber instruments dual probe PID. I've threaded one thermometer probe into a shoelace which is dipped in a water container so that the thermometer is reading as a wet bulb. I've set the PID to use this wet bulb temp to control the smoker's heating element. The second PID probe measures dry bulb temp, and I use a wireless thermometer to measure the meat's IT.

I set the smoke for 7 hours and the 'wet bulb' temp at 135F. After 7 hours the IT of the pork was 171F (I didn't monitor the IT during the smoke, so I don't know whether there was a stall). I vacuum sealed it and put it into my sous vide set up (A Fresh Meals Magic immersion heater with bubbler controlled by the PID) at 150F for the next 2 days.

The results were good, but I am unsure of my smoking method. Is this the correct method of using the wet bulb thermometer method? I'm concerned that the IT of the pork went up too high during the smoke as the heating element was always being controlled by a wet bulb. I don't see a way that I can program my PID to switch to using the dry bulb probe short of physically switching them once the meat's IT reaches 135F (which I can do because I can set an alarm to alert me using my wireless thermometer).

Would it have been been better to somehow add a step on the PID (I will have to see if I can program it that way) to hold temp the IT temp at 135F once this was reached? Since I can't precisely control relative humidity other than keeping the water pan full, do you have any thoughts as to how to improve on my method?

Edited June 9, 2012 by Neekerbocker (log)

[Chris Hennes]

I'm not Nathan (obviously!) but I was just re-reading this section of Modernist Cuisine this morning in preparation for making some pastrami: 135°F is the wet-bulb temp they recommend there, and I think your method of measuring it is a good one. They suggest a dry-bulb temperature of 150°F at 65% RH: clearly your dry bulb was considerably higher than this. The key I think is that you don't want the internal temp to rise above the temperature you are going to sous vide it at (in your case 150°F), so when it comes up near that you will want to drop your smoker temperature down, or take the meat out (if you think it's had enough smoke).

[Martin Fisher]

This is always a fascinating subject!

FWIW, Here are NOAA's Relative Humidity/Dew Point tables for various elevations for anyone who may have a special interest.

~Martin