Post by theropod on Aug 3, 2019 17:03:18 GMT 5
DISCLAIMER: I intend to make this thread into a sort of "zoological and palaeobiological general knowledge" directory so we can share essential knowledge that is usually presupposed. Of course, feel free to add your own posts if you have important subjects you think need to be adressed, just make sure to keep it to general overviews or concepts with wide applicability so this initiative doesn’t become too cluttered. E.g. a general introduction to tetrapod systematics or palaeobiology would have a place here, but not a discussion of a particular taxon, or, FSM forbid, some sort of fight scenario.
Directory:
Physics and Mathematics
Force vs Pressure – this post (see below)
Power vs Force→
Scaling→
creature386 : Principal Component Analysis→
creature386 : An Introduction to Applied Statistics→
Functional Morphology
Infinity Blade : Animal head weaponry: form and function→
Infinity Blade : "Bird bones are hollow"→
The difference between force and pressure, and why 'psi' is not 'bite force'
Force and pressure are not the same thing. Force is mass times acceleration, or work per distance. Pressure is force per area.
A muscle contraction generates a force in the direction it contracts. If it acts to close a jaw, that jaw produces a force, dependant on the relative distances of the muscle insertions and the point where the output force is measured from the jaw joint (the mechanical advantage of the muscle) and the line of action of the muscle relative to the direction of jaw closure. That is also where the range of force figures for different points along the jaw comes from, any why it’s usually less in the front teeth than in the back, where the mechanical advantage is greatest.
That force is the bite force. It is measured in Newtons (kgms⁻²), or in the force-equivalent of kilograms or tons (under standard earth gravity, usually rounded to 10ms⁻²).
As an animal gets bigger, forces it produces will grow to the 2nd power of length. I.e. if your theropod is 12m long, its bite force will be 4 times that of a geometrically similar 6m theropod.
A force applied over an area produces a pressure. Pressure is measured in Pascals, Newtons per square meter (Nm⁻²), or for our purposes more commonly in kilopascals, megapascals or gigapascals. Certain people like to use psi, but you are unlikely to find this unit in scientific sources.
As an animal gets bigger, the pressure doesn’t necessarily become any greater. That’s because both the force it produces, and the area over which it is applied, grow at the same speed (2nd power). A 12m theropod will have 4 times the bite force of a 6m one, but its bite will also cover 4 times the area, so the resulting pressure is the same.
There is one caveat to that, namely geometrically different jaw and tooth morphologies and the error inherent in trying to compare them.
For one, a larger animal might compensate for its relatively greater size by having proportionately larger muscles, which would generate a higher force.
Secondly, a larger animal might not necessarily have blunter tooth tips or edges, even if the teeth are larger overall, so a given distance from the tips, the area might indeed be similar. In that case, initial tooth pressures might be higher, but as soon as the teeth have penetrated by the same amount relative to their size, it will be the same. The deeper the tooth penetrates, the greater the cross-sectional area the force is applied over, the lower the pressure becomes, until it is so low the tooth can no longer penetrate further.
The pressure is not a property specific to that animal’s bite, unlike the force, but rather a result of specific assumptions about behaviour and circumstances of a bite. Now if two animals have different jaws and teeth, it is pretty much impossible to objectively compare them. Say you wanted to compare a T. rex bite to a lion’s. It is straightforward to say the T. rex bites X times harder in terms of force. Does it generate higher pressures? That depends on your assumptions. If you assume both focus their bite force on the same small area, of course it would. But if you assume they both focused their bite force on the same percentage of the area inside their mouths, or the area of their teeth, then things might look completely different. So pressure is very misleading if we aren’t given precise information on what area the figure refers to.
Of course pressure can be important, e.g. in terms of the capacity to penetrate something of known strength properties. I have already presented examples elsewhere, but take a tooth of known geometry. Since we know the material properties of bone, if we know the bite force, we can estimate how deeply such a tooth could penetrate bone. However we can only do that if we know the actual force of the bite, not some arbitrarily derived figure for the pressure over some unknown area. Yet again, this exemplifies how misleading pressure will be without knowing the area, because lots of animals can generate pressures sufficient to puncture bone, but this gives us no information on how large that puncture will be. Being stabbed with a syringe isn’t the same as being stabbed with a sword, yet both require the same pressure to break human skin, it’s just that the sword is far larger and thus needs far more force to generate that pressure, but also delivers a far larger wound.
It is also important to keep in mind the limitations of the materials in question. Bone has a compressive strength of less than 200 MPa, and tooth enamel has a compressive strength of less than 400 MPa. So any pressure greater than those is impossible to achieve without the use of stronger materials than are available in the vertebrate body. And these materials don’t become stronger (at least not much) in larger animals, so the limit remains the same. You cannot generate a higher pressure with a tooth pressing into bone, because pressure depends on area and force, and force always entails an equal and opposite counterforce. So if a tooth only experiences a resistance of 200MPa, even if the bite force and small area of the tooth would theoretically allow to generate a pressure of 2000MPa, the real pressure will still only be 200MPa, because that pressure is enough to shatter whatever bone it bit into.
Meaning in effect, that no vertebrate ever generated a bite pressure higher than the compressive strength of cortical bone, no matter what theoretical bite pressure some study estimated over some somewhat arbitrarily defined area.
If a crocodile's bite pressure is estimated at 1000MPa 1mm from the tooth tip, all that means is that the crocodile could bite into bone (a lot) deeper than 1mm, because crushing the bone would only require a fraction of that theoretical pressure.
Directory:
Physics and Mathematics
Force vs Pressure – this post (see below)
Power vs Force→
Scaling→
creature386 : Principal Component Analysis→
creature386 : An Introduction to Applied Statistics→
Evolution and Phylogenetics
Functional Morphology
Infinity Blade : Animal head weaponry: form and function→
Infinity Blade : "Bird bones are hollow"→
Technology
OK guys, I keep saying this, but people keep conflating the two, so maybe we can put this to rest this way.
The difference between force and pressure, and why 'psi' is not 'bite force'
Force and pressure are not the same thing. Force is mass times acceleration, or work per distance. Pressure is force per area.
A muscle contraction generates a force in the direction it contracts. If it acts to close a jaw, that jaw produces a force, dependant on the relative distances of the muscle insertions and the point where the output force is measured from the jaw joint (the mechanical advantage of the muscle) and the line of action of the muscle relative to the direction of jaw closure. That is also where the range of force figures for different points along the jaw comes from, any why it’s usually less in the front teeth than in the back, where the mechanical advantage is greatest.
That force is the bite force. It is measured in Newtons (kgms⁻²), or in the force-equivalent of kilograms or tons (under standard earth gravity, usually rounded to 10ms⁻²).
As an animal gets bigger, forces it produces will grow to the 2nd power of length. I.e. if your theropod is 12m long, its bite force will be 4 times that of a geometrically similar 6m theropod.
A force applied over an area produces a pressure. Pressure is measured in Pascals, Newtons per square meter (Nm⁻²), or for our purposes more commonly in kilopascals, megapascals or gigapascals. Certain people like to use psi, but you are unlikely to find this unit in scientific sources.
As an animal gets bigger, the pressure doesn’t necessarily become any greater. That’s because both the force it produces, and the area over which it is applied, grow at the same speed (2nd power). A 12m theropod will have 4 times the bite force of a 6m one, but its bite will also cover 4 times the area, so the resulting pressure is the same.
There is one caveat to that, namely geometrically different jaw and tooth morphologies and the error inherent in trying to compare them.
For one, a larger animal might compensate for its relatively greater size by having proportionately larger muscles, which would generate a higher force.
Secondly, a larger animal might not necessarily have blunter tooth tips or edges, even if the teeth are larger overall, so a given distance from the tips, the area might indeed be similar. In that case, initial tooth pressures might be higher, but as soon as the teeth have penetrated by the same amount relative to their size, it will be the same. The deeper the tooth penetrates, the greater the cross-sectional area the force is applied over, the lower the pressure becomes, until it is so low the tooth can no longer penetrate further.
The pressure is not a property specific to that animal’s bite, unlike the force, but rather a result of specific assumptions about behaviour and circumstances of a bite. Now if two animals have different jaws and teeth, it is pretty much impossible to objectively compare them. Say you wanted to compare a T. rex bite to a lion’s. It is straightforward to say the T. rex bites X times harder in terms of force. Does it generate higher pressures? That depends on your assumptions. If you assume both focus their bite force on the same small area, of course it would. But if you assume they both focused their bite force on the same percentage of the area inside their mouths, or the area of their teeth, then things might look completely different. So pressure is very misleading if we aren’t given precise information on what area the figure refers to.
Of course pressure can be important, e.g. in terms of the capacity to penetrate something of known strength properties. I have already presented examples elsewhere, but take a tooth of known geometry. Since we know the material properties of bone, if we know the bite force, we can estimate how deeply such a tooth could penetrate bone. However we can only do that if we know the actual force of the bite, not some arbitrarily derived figure for the pressure over some unknown area. Yet again, this exemplifies how misleading pressure will be without knowing the area, because lots of animals can generate pressures sufficient to puncture bone, but this gives us no information on how large that puncture will be. Being stabbed with a syringe isn’t the same as being stabbed with a sword, yet both require the same pressure to break human skin, it’s just that the sword is far larger and thus needs far more force to generate that pressure, but also delivers a far larger wound.
It is also important to keep in mind the limitations of the materials in question. Bone has a compressive strength of less than 200 MPa, and tooth enamel has a compressive strength of less than 400 MPa. So any pressure greater than those is impossible to achieve without the use of stronger materials than are available in the vertebrate body. And these materials don’t become stronger (at least not much) in larger animals, so the limit remains the same. You cannot generate a higher pressure with a tooth pressing into bone, because pressure depends on area and force, and force always entails an equal and opposite counterforce. So if a tooth only experiences a resistance of 200MPa, even if the bite force and small area of the tooth would theoretically allow to generate a pressure of 2000MPa, the real pressure will still only be 200MPa, because that pressure is enough to shatter whatever bone it bit into.
Meaning in effect, that no vertebrate ever generated a bite pressure higher than the compressive strength of cortical bone, no matter what theoretical bite pressure some study estimated over some somewhat arbitrarily defined area.
If a crocodile's bite pressure is estimated at 1000MPa 1mm from the tooth tip, all that means is that the crocodile could bite into bone (a lot) deeper than 1mm, because crushing the bone would only require a fraction of that theoretical pressure.
