...alternately titled "An Exercise in Needless Precision"
So, I breed-changed this Snapper from a Tundra a couple days ago, unfortunately forgetting to record any previous data:
I don't really know much about Snappers overall (this is my first one that wasn't bought as exalt fodder), but that seemed...a bit small, volume wise. I was curious about how things like the square/cube law and flight (or maybe swimmingI guess since I do NOT want to do the math for gravity that's a lie I told myself when I started typing this out) would impact him, but then I ran into the problem that you can't really do anything with weight. Like, sure I guess it's close enough to mass if you don't really care about pinpoint accuracy and a reasonable number of significant digits. However, since most calculations require mass which is different, here I went.
To get mass from weight, you need to know both the weight of your object, and the acceleration due to gravity. Weight? Check. 1211.85 KG. Gravity? Not so check.
We know that Sornieth's got slightly less gravity cause Reasons, straight from the horse's mouth:
[source][more details over here]
So. This means we can't just swap in earth's snazzy 9.8 m/s2 and be completely accurate (to at least two decimal places). Fortunately, with the help of Newton and Google, we can calculate this for Sornieth. And then get back to actually massing my Snapper.
To calculate the acceleration due to gravity, represented as little "g" because I'm tired of writing it out, we need the universal gravitational constant (G), the mass of the thing whose gravity we're checking (Sornieth), and the radius of that thing (Sornieth); all to plug into this equation:
g = (G * MSornieth) / rSornieth2
G is universal and since it's been Strongly Implied that physics is still a thing, I'm going to assume stuff like lightspeed and the fundamental forces of nature are the same in the FR world and that the universal constants remain universal, barring Arcanist, which means that we can assume G = 6.67408 × 10-11 m2 / kgs2 s2
Assuming "roughly one and a half times" the radius can be safely treated as avg(rSornieth) = 1.5rEarth since the Earth's radius is an average measurement anyway... this gives us rSornieth = 9556500m = 9556.5km = 6371km * 1.5 = rEarth * 1.5, our equation for g now looks like this:
g = (6.67408 × 10-11 m2/ kgs2 s2 * MSornieth) / (9556500m)2
This still leaves MSornieth. Fortunately for me, @catgame21234 and co have already done SO MUCH working out over in [this thread] that I'm just going to trust them to have this done toa reasonable degree of accuracy almost a reasonable, and take their figure for MSornieth = 2.01 × 1025 kg, but substitute 2.01 × 1024 kg for it, assuming the 1025 was a typo since... 2.01 × 1025 kg is greater than 5.972 × 1024 kg which implies MSornieth > MEarth, which is in turn directly contradicted by the base assumptions from the lore. However! This still means our equation is now down to one variable, and can then be solved for g:
g = (6.67408 × 10-11 m2 / kg2 s2 * 2.01 × 1024kg) / (9556500m)2
So! gSornieth = 1.46889156604 m / s2. That's definitely less than Earth's! For reference, gLuna = 1.6 m / s2, so we know that walking around on Sornieth is basically like walking around on Earth's moon, since human perception proooobably isn't good enough on all models to detect a 0.04 m / s2 difference. That's one mystery solved. Back to my Snapper.
Weight is given by the site mechanics itself, however kilograms are measures of mass, not weight (as I have found out just now through aggressive googling). I'm going to assume that, because this is an exercise in Needless Precision, this is actually a unit in kilogram force, or kp (kilopond). 1 kp = 9.806650 N which is....a lot of Newtons. Thanks Newton.
To calculate the weight of an object from mass and g, you use the following equation and get a result in N (Newtons), since weight is really a measure of the force of how much the heavier thing you're standing on Really Really Wants You:
w (in N) = m (in kg) * g (in m / s2)
Fortunately, because algebra, we can twist this around to give a result for mass:
m = w / g
The weight of my Snapper, or force it would exert on a scale, is 11884.1888025 N = 1211.85 * 9.806650. Since we've gotten gSornieth, we can solve this equation for mSnapper:
m = w / g
Wow. Okay. That is... a lot. MSnapper = 8090.583 kg, which is going to give us some TERRIFYING density results.
Density = Mass * Volume.
We have mass. Now, to get volume! Volume is a pretty simple calculation of length * width * height. Or would be, if our snapper were a simple cuboid. We are, however, going to assume it has a uniform density because there's only so much unnecessary calculating I can handle.
Making the assumption that dragon length is measured from nosetip to tailtip, this is given as 1.84 m. This is helpful for the overall calculation, but not for determining the other two values, since the art is clearly angled slightly with the head of the dragon closer to the viewer. I've taken the model Snapper female into an image editor and taken some pixel measurements of relevant distances:
red = 82.4px
yellow = 41.2px
green = 66.0px
blue = 91.5px
cyan = 8px
magenta = 219.0px
Going by the same standard for measuring wingspan, we now have a real number to map onto these measurements, 1.21m. I'm treating this as a sound converstion because width varies more with perspective than height, and at the perspective depth of the first wing any accuracy lost will be negligible as all but one of these measurements will be taken at roughly the same part of the dragon.
wingtip to wingtip = (yellow + green + blue + cyan + magenta) * 2
1.21m = (41.2px + 66.0px + 91.5px + 8px + 219.0px) * 2
÷851.4
0.00142118863 = 1px
Now we have a measuring stick!
white = 129.0px
black = 99.0px
Assuming that the dragon can scrunch up its legs and make like a turtleand any seemingly Too Small-Ness on the front will account for in the extra area included along the tail, this gives us a height of 0.14069767437m = 99.0 * 0.00142118863 and a width of 0.18333333327m = 129.0 * 0.00142118863.
VSnapper = LSnapper * WSnapper * HSnapper
So! At long last, since Density = Mass * Volume, we can plug in the two known values after all this tedium, and get the following, assuming uniform density of the dragon since we don't even know if they're carbon based let alone whatever else they're made of.
D = 8090.583 kg * 0.0475 m3
DensitySnapper = 384.3 m3 kg. Yay! Now we know. I have no idea what to use this information for, but I sure do know it now. To a truly unnecessary level of detail.
Funnily enough, plugging in the given weight (as mass) and length of this dragon and doing some hazy estimation for width and height (w = 2 ( (wingspan / 2) / 5) = 0.242, h = (2/3) * ( (wingspan / 2) / 5) * 4) = 0.726),
D = (1211.85 kg) * (1.84m * 0.242m * 0.726m)
Which is probably close enough to the longer calculation for all practical scientific purposes in this game.
I would advice NOT doing the weight conversions in future calculations since if you don't it probably won't affect accuracy too much and I feel like I've done something...unnecessary. Which, despite being one of the two points of this thread, isn't in fact necessary for general details. The acceleration due to gravity/gravitational force info is cool and probably actually useful, though.
thanks for coming to my TED talk
So, I breed-changed this Snapper from a Tundra a couple days ago, unfortunately forgetting to record any previous data:
 |
measurements wrote:
Length: 1.84M
Wingspan: 1.21M Weight: 1211.85KG |
I don't really know much about Snappers overall (this is my first one that wasn't bought as exalt fodder), but that seemed...a bit small, volume wise. I was curious about how things like the square/cube law and flight (or maybe swimming
To get mass from weight, you need to know both the weight of your object, and the acceleration due to gravity. Weight? Check. 1211.85 KG. Gravity? Not so check.
We know that Sornieth's got slightly less gravity cause Reasons, straight from the horse's mouth:
Aequorin wrote:
The size of Sornieth is larger than Earth (roughly one and a half times the radius). It has slightly less gravity. Whether that's due to its mass and the make-up of its core or the influence of magical fields is still a matter of draconic debate!
So. This means we can't just swap in earth's snazzy 9.8 m/s2 and be completely accurate (to at least two decimal places). Fortunately, with the help of Newton and Google, we can calculate this for Sornieth. And then get back to actually massing my Snapper.
To calculate the acceleration due to gravity, represented as little "g" because I'm tired of writing it out, we need the universal gravitational constant (G), the mass of the thing whose gravity we're checking (Sornieth), and the radius of that thing (Sornieth); all to plug into this equation:
g = (G * MSornieth) / rSornieth2
G is universal and since it's been Strongly Implied that physics is still a thing, I'm going to assume stuff like lightspeed and the fundamental forces of nature are the same in the FR world and that the universal constants remain universal, barring Arcanist, which means that we can assume G = 6.67408 × 10-11 m2 / kgs2 s2
Assuming "roughly one and a half times" the radius can be safely treated as avg(rSornieth) = 1.5rEarth since the Earth's radius is an average measurement anyway... this gives us rSornieth = 9556500m = 9556.5km = 6371km * 1.5 = rEarth * 1.5, our equation for g now looks like this:
g = (6.67408 × 10-11 m2/ kgs2 s2 * MSornieth) / (9556500m)2
This still leaves MSornieth. Fortunately for me, @catgame21234 and co have already done SO MUCH working out over in [this thread] that I'm just going to trust them to have this done to
g = (6.67408 × 10-11 m2 / kg2 s2 * 2.01 × 1024kg) / (9556500m)2
= 1.3414901 × 1014 m2 kg2 / kg s2 / (9556500m)2
= 1.3414901 × 1014 m2 kg / kg2 s2 / 9.1326692 × 1013 m
= 1.46889156604 m2 kg / kg2 s2 m
= 1.46889156604 m2 kg / kg2 s2 m
= 1.46889156604 m / s2
where did the extra kg go? I don't know. I asked my friend who is way smarter than me and they said "That's physics for you" so I guess. it probably wasn't important. units are lies. there's also an implicit N in there somewhere but it's ignored for probably the same reason
So! gSornieth = 1.46889156604 m / s2. That's definitely less than Earth's! For reference, gLuna = 1.6 m / s2, so we know that walking around on Sornieth is basically like walking around on Earth's moon, since human perception proooobably isn't good enough on all models to detect a 0.04 m / s2 difference. That's one mystery solved. Back to my Snapper.
Weight is given by the site mechanics itself, however kilograms are measures of mass, not weight (as I have found out just now through aggressive googling). I'm going to assume that, because this is an exercise in Needless Precision, this is actually a unit in kilogram force, or kp (kilopond). 1 kp = 9.806650 N which is....a lot of Newtons. Thanks Newton.
To calculate the weight of an object from mass and g, you use the following equation and get a result in N (Newtons), since weight is really a measure of the force of how much the heavier thing you're standing on Really Really Wants You:
w (in N) = m (in kg) * g (in m / s2)
Fortunately, because algebra, we can twist this around to give a result for mass:
m = w / g
The weight of my Snapper, or force it would exert on a scale, is 11884.1888025 N = 1211.85 * 9.806650. Since we've gotten gSornieth, we can solve this equation for mSnapper:
m = w / g
= 11884.1888025 N / 1.46889156604 m / s2
= 8090.58277497 kg
which we are rounding way the heck down to 8090.583 kg, and units? what units. don't worry about it.
Wow. Okay. That is... a lot. MSnapper = 8090.583 kg, which is going to give us some TERRIFYING density results.
Density = Mass * Volume.
We have mass. Now, to get volume! Volume is a pretty simple calculation of length * width * height. Or would be, if our snapper were a simple cuboid. We are, however, going to assume it has a uniform density because there's only so much unnecessary calculating I can handle.
Making the assumption that dragon length is measured from nosetip to tailtip, this is given as 1.84 m. This is helpful for the overall calculation, but not for determining the other two values, since the art is clearly angled slightly with the head of the dragon closer to the viewer. I've taken the model Snapper female into an image editor and taken some pixel measurements of relevant distances:
red = 82.4px
yellow = 41.2px
green = 66.0px
blue = 91.5px
cyan = 8px
magenta = 219.0px
Going by the same standard for measuring wingspan, we now have a real number to map onto these measurements, 1.21m. I'm treating this as a sound converstion because width varies more with perspective than height, and at the perspective depth of the first wing any accuracy lost will be negligible as all but one of these measurements will be taken at roughly the same part of the dragon.
wingtip to wingtip = (yellow + green + blue + cyan + magenta) * 2
1.21m = (41.2px + 66.0px + 91.5px + 8px + 219.0px) * 2
= 425.7px * 2
= 851.4px
÷851.4
0.00142118863 = 1px
Now we have a measuring stick!
white = 129.0px
black = 99.0px
Assuming that the dragon can scrunch up its legs and make like a turtle
VSnapper = LSnapper * WSnapper * HSnapper
= 1.84 m * 0.18333333327 m * 0.14069767437 m
= 0.0475 m3
albeit truncated to the accuracy of our loosest measurement. at long last, units that make some bloody sense.
So! At long last, since Density = Mass * Volume, we can plug in the two known values after all this tedium, and get the following, assuming uniform density of the dragon since we don't even know if they're carbon based let alone whatever else they're made of.
D = 8090.583 kg * 0.0475 m3
= 384.3026925 m3 kg
DensitySnapper = 384.3 m3 kg. Yay! Now we know. I have no idea what to use this information for, but I sure do know it now. To a truly unnecessary level of detail.
Funnily enough, plugging in the given weight (as mass) and length of this dragon and doing some hazy estimation for width and height (w = 2 ( (wingspan / 2) / 5) = 0.242, h = (2/3) * ( (wingspan / 2) / 5) * 4) = 0.726),
D = (1211.85 kg) * (1.84m * 0.242m * 0.726m)
= (1211.85 kg) * (0.32327328 m3)
= 391.8 m3 kg
Which is probably close enough to the longer calculation for all practical scientific purposes in this game.
Summary / Teal Dear: wrote:
|
Gravity on Sornieth: Density of this Snapper: ...without all that work: |
1.46889156604 m / s2 384.3026925 m3 kg 391.8 m3 kg |
I would advice NOT doing the weight conversions in future calculations since if you don't it probably won't affect accuracy too much and I feel like I've done something...unnecessary. Which, despite being one of the two points of this thread, isn't in fact necessary for general details. The acceleration due to gravity/gravitational force info is cool and probably actually useful, though.
thanks for coming to my TED talk
|
he/him FR+1 lightningy link ->____________________________________________________________ |
|
click for sound + source 
