
Weighing a Car with Tire Pressures - as89
https://surjan.substack.com/p/16-weighing-a-car-with-tire-pressures
======
jedberg
> The first thing I wanted to do with my Saab 96 was to establish a baseline
> weight. The cheapest scales used for racing are over $700,

You can do this for (almost) free if you go to the local dump. They usually
charge you based on weight of what you dump by weighing your car on the way in
and on the way out.

Just ask them what the reading is on the way out. If you bring a couple of
pounds of garbage, it will cost a few dollars at most.

~~~
crazyjncsu
Or go to the metal scrapyard instead, and leave with a few dollars more than
you came with! (and get weighed) .. and if you have a pickup truck, you get to
see them use this cool magnet to suck your junk out of the bed ;)

~~~
jedberg
When I would bring stuff to the dump, I would see people pick up all the metal
items from the pile after they dump their trash. It would add weight to their
car, so they were charged less, and then they could recycle the metals for
even more money. I found it to be a brilliant system. Not entirely sure if
it's fraud or not...

~~~
HPsquared
Theft followed by fraud I think. Edit: or maybe the fraud occurs at the weigh
scales and the theft occurs at the exit gate? IANAL

------
joosters
Another way to possibly get better accuracy is to pump the tyres to several
different pressures, and for each pressure, re-measure the tyre contact
surface.

From there, you could then simply average out the results - or better still,
the data would help you reason about the pressure<->area relationship. Just
going by the P=F/A formula, pressure should be inversely proportional to area,
but people have pointed out things like the tyre sidewall stiffness will
affect this. Taking several pressure<->area measurements would help you reason
about this - perhaps the sidewall means P = F/A + x, and with multiple
datapoints, 'x' can be calculated.

~~~
spuz
I was thinking the same but I imagine you'd have to buy a tyre pump as well in
order to re-inflate the tyres. Not sure how much they would cost...

~~~
barrkel
A 12v pump which plugs in to a cigarette lighter socket costs about $15 / 12
GBP. They're not the fastest things in the world but they work and there's no
labour other than screwing them on and off.

------
ColinWright
I'm late to the game, and probably no one will see this, but I thought I'd
mention that I tweeted about this back in 2017:

[https://twitter.com/ColinTheMathmo/status/870678851390537728](https://twitter.com/ColinTheMathmo/status/870678851390537728)

The ensuing discussion was wide-ranging, and covered various limitations of
this technique. It was more true of older tires, but tires now have more
structure, so some of the car's weight is supported by the tire structure, and
not just by the air pressure.

In turn, I remember reading about this in a Martin Gardner book, probably
nearly 40 years ago.

~~~
njsubedi
You made it to the top of the comments section.

~~~
ColinWright
That's ... genuinely surprising ... thanks for letting me know!

(Sorry people are downvoting you for that, I appreciated it.)

------
metaphor
> _I have a decent pressure gauge that I got for $25, so I feel I can be
> reasonably accurate._

Such a false sense of confidence for a product[1] whose actual performance
specs aren't properly published. And it isn't just Longacre playing this game.

If you're in the recreational motorsports scene, you've probably noticed what
I'm referring to. If you're an engineer in the same, it probably has driven
you nuts. I'm not even talking about full NIST traceability (although if a
serious customer wants that and is willing to pay, it shouldn't be an
issue...good luck with that) but just a really basic warm and fuzzy.

Intercomp[2] pulls the "Certified Accuracy" bullshit marketing wank, but
doesn't even specify the overarching standard that their products are
certified against.

Joes Racing[3] labels their analog "Pro" model as "ANSI grade B40.1", but if
you've actually read ASME B40.1 proper (currently published in ASME
B40.100-2005, which contains 5 related standards including B40.7 for digital
gauges), you'd know that's bullshit marketing wank...for all anyone knows,
they're selling pseudo-Grade D chinesium trash at a premium price point.

Pick any consumer-grade product and you'll discover the same pattern.

The only markets I've seen any semblance of meaningful published
specifications with respect to pressure gauges are industrial and
scientific/metrology. Of course, the typical players in those markets aren't
nearly as naive.

[1]
[http://www.longacreracing.com/products.aspx?itemid=1716&prod...](http://www.longacreracing.com/products.aspx?itemid=1716&prodid=95479&pagetitle=Basic-2%22-Tire-
Gauge)

[2]
[https://www.intercompracing.com/documents/Literature/7005110...](https://www.intercompracing.com/documents/Literature/7005110%20Air%20Pressure%20Gauges%20SR.pdf)

[3] [https://www.joesracing.com/product/joes-pro-tire-
gauges/](https://www.joesracing.com/product/joes-pro-tire-gauges/)

~~~
YarickR2
Any recommendations for decently precise tire gauges ?

~~~
parimm
Digital ~230 USD - [https://www.mcmaster.com/pressure-gauges/pressure-and-
vacuum...](https://www.mcmaster.com/pressure-gauges/pressure-and-vacuum-
gauges/digital-high-accuracy-pressure-gauges/)

Analog gauge ~100 USD -[https://www.mcmaster.com/pressure-gauges/pressure-and-
vacuum...](https://www.mcmaster.com/pressure-gauges/pressure-and-vacuum-
gauges/pressure-gauges-9/)

Both of the above gauges come with Calibration Certificate Traceable to NIST

------
function_seven
How much does tire sidewall stiffness contribute to the force holding the car
up? I know that can vary a lot. Some cars have run-flats that won't sag when
they lose pressure (or won't sag as much, anyway). Low profile tires probably
transfer more of the load through the sidewall than doughnut tires.

And of course the contribution from the sidewalls (as a percent) will change
as tire pressure increases.

~~~
surjansingh
Oops that's a great point. I completely forgot about sidewall stiffness. My
messing around with treads was probably just me adjusting things to make
myself look good then!

~~~
pdog
Don't worry. Fiddling with your one free parameter to make your model look
good is as quintessential to statistics as Student's t-distribution.

------
SigmundA
Commercial trucks with air suspension do this, there are various "on-board"
scales that tap into the air lines and try and give a weight. It's obviously
much more of an issue when you have regulations involved in how much you can
carry, so weighing is a big part of trucking.

Here are a few:

[https://www.air-weigh.com](https://www.air-weigh.com)

[https://rwls.com](https://rwls.com)

[https://www.appweigh.com](https://www.appweigh.com)

There are many.

~~~
FractalParadigm
Bingo, came in to throw my two cents out as a driver. Only difference between
the OP and trucks is that trucks typically measure the pressure in the
suspension (virtually all trucks built in the last 20 years use air
suspension, at least for the rear axles), which gives a surprisingly accurate
reading.

 _Most_ of the trucks I've driven have either an analog "rear suspension
pressure" gauge, or a digital calculation of _approximately_ how much weight
is there for the given pressure. With an analog gauge, you as a driver start
to get a better idea of how much weight is on your drives, possibly saving
yourself from shelling out $20 to scale up on a regular basis. As I sit in my
truck without a trailer, I currently have a reading of ~10psi; this truck for
instance, every additional ~5k lbs over the drives is an additional ~10 psi in
the bags.

------
mauvehaus
Relatedly: if you and your bicycle weigh 200 pounds, and your tires are
inflated to 90 psi (a very reasonable pressure for a road bike; racers run
much skinnier higher pressure tires), your total contact patch is a little
over 2 square inches. Think about that the next time you’re watching somebody
fly down a descent going 45mph or more. That’s not a lot of rubber keeping you
on course.

As an added bonus, you can basically ignore sidewall stiffness for bicycle
tires.

~~~
kevin_thibedeau
All the leet roadies are running 25mm tires now. You get jibed for running
23's on an older bike with brakes that don't open enough.

~~~
zten
25 is already oldschool. Newest aero rims are designed for 30+, running
absurdly low pressures with hookless tubeless tires.

~~~
mauvehaus
I guess I'm way out of date. I remember hearing that people who ride e.g. PBP
run way wider tires than normal road racers because of the road conditions,
but I didn't realize that the mainstream road racers were running that wide
now.

Also: hookless? Like they got rid of in, like, the '70s or '80s? My beater
road bike (that's older than I am) has 630mm hookless rims, and I got a
discount because of it.

Are the new ones hell to change tires on? Changing tires on that bike is the
most miserable bike maintenance task I've done. And I've done most anything
short of a headset or suspension fork rebuild.

~~~
zten
Well, a lot of this is driven by the gravel racing gang... the people partying
at gravel events are already happy running 40+mm width, or MTB tires, on very
wide rims. But there's also a growing segment of people who have figured out
that you can have a bike that's a little bit more comfortable off pavement by
going wider, without totally compromising speed on the pavement, and it also
makes tubeless less likely to blow up in your face.

Zipp and ENVE seem to be in some kind of internal width arms race with the
release of the Zipp 303-S, and the ENVE SES AR series rims. I was exaggerating
a little bit :) You'll still find many, many road bikes with disc brakes
maxing out with clearance for 32mm width, but that's an improvement over their
rim brake cousins. But look around in the growing "all-road" segment and
you'll find wider tire clearances on road geometry frames showing up.

I am unsure if this hookless is the same hookless that is from way back in the
day. With the way things go in the bike industry (cyclically, no pun
intended), I wouldn't be surprised if it were.

~~~
mauvehaus
That was informative; thank you. I’ve been pretty out of touch with the
cutting edge for a while.

> I am unsure if this hookless is the same hookless that is from way back in
> the day. With the way things go in the bike industry (cyclically, no pun
> intended), I wouldn't be surprised if it were.

I’m sure they’re holding way tighter tolerances in manufacturing now than they
were back then at the very least. Probably more on the tire side than the rim
side.

You used to have to get matched sets of V-belts for multi-belt applications,
table saws being a common one.

Nowadays, people mostly accept that the tolerances are tight enough that you
don’t need to do that, at least for the lighter-duty uses.

------
cryptoz
You can weigh small objects with most smartphones with decent accuracy these
days using the barometer. Put your phone into a ziplock bag, blow full of air,
zip closed. Take a small object with known weight to calibrate your scale.
Carefully place the object on the ziplock bag with your phone inside. The
barometer in your phone can measure the air pressure change by having the
weight placed on top of the bag. Knowing the weight of your first object and
the change in pressure observed, you can calibrate the scale to know how much
pressure change correlates to weight placed on top.

Then you can weigh arbitrary objects using your phone! Be careful, don't break
your phone (don't try to stand on it to weigh yourself!)

~~~
perl4ever
On measuring things - I prefer going in the opposite direction and weighing
even where it's unconventional.

I have a Melitta funnel for making single servings of coffee, but when I'm
using it I can't see how full my mug is without lifting up, and they are
mostly opaque, and the funnel doesn't hold a full mug's worth of water. So I
started putting my mug, funnel, filter, and coffee on a digital scale with
tare, and remembering how much each size holds in dry ounces. It avoids the
situation in which I'm waiting for the water to run out to make sure it won't
overflow; I just pour until I hit the right weight and then go do something
else until it's done.

------
dognotdog
Kudos, for My first inclination would've been to jack up the car and look at
pressure differences of unloaded vs. loaded tyres... then look at loaded wheel
center height above ground vs. nominal radius, compute the the reduction in
volume, and assume contact patch to be the area of the flattened section of
the tyre cylinder... giving me a whole lot of parameters with wild
inaccuracies and probably equally wild results :)

------
calvinmorrison
I don't often open HN and see a Saab 96 post. I have many Saabs but by far my
96 is my favorite.

A V4, yes V in a car A compact 4 speed transaxle with 4 on the tree

So much fun. Torquey. Enjoyable. Gets good looks and sparks conversation

Easy to work on!

I do love my 900s as my daily drivers but the 96 is a masterpiece

------
pedalpete
Back when Microsoft was doing those obscure job interview questsions like "how
much does a 747 weigh", this was my solution, measure the deflection of the
tires and the PSI to calculate weight. Apparently the answers they were
looking for were more along the lines of "put the plane on an aircraft carrier
in a lake and measure the water displacement" <shrug>

~~~
justanotherc
Lol, my question to that would have been how do you get the 747 on the
aircraft carrier?

That's actually a harder question than getting the weight of one... which
makes the entire exercise ridiculous.

------
abstrakraft
This method doesn't account for the support of the tire itself through the
sidewalls, as opposed to the pressure contained within it.

You should be able to estimate this contribution by fitting to the curve of
area vs pressure at lower pressures. For example, the linear F=PA relationship
clearly breaks down at 0 pressure, as F>0 and A>0 when P=0.

~~~
basicplus2
Except (as mentioned further up this post) when the side walls are in tension
due to the air pressure within the tyre.

------
JoshuaDavid
I wonder if you could do even better by putting paint or ink on the outside of
the tire, driving over a piece of paper, and seeing what fraction of the paper
touched your tire (and thus what fraction of the rectangle boundary actually
touches the ground).

~~~
dmurray
And to measure how much of the grooves are in contact with the ground, you
could add a known weight to the car (like 100kg of people), measure it with
and without that weight and see what proportion of the grooves you need to
account for to get 100kg difference.

You'd get better accuracy from a bigger added weight, but the bigger the added
weight the more you risk changing what you're measuring by forcing more tire
rubber into contact with the ground.

------
frank2
If you drive the tire onto a rail half as wide as the width of the tire
(specifically, the width of the area in contact with flat ground), then
according to his logic, the length of rail in contact with the tire will be
twice the length of flat ground in contact with the tire (assuming the contact
area to be roughly rectangular in each case). I have no doubt that the length
would be more, but severely doubt it would be anything close to twice as much
because I think a large percentage of the "normal force" (the weight of the
car) goes into keeping the tire bent out of shape in ways that do not
contribute linearly to the area in contact with the rail.

My guess is that the tire's resistance to being bent out of shape is also a
significant factor in the usual case of the tire's resting on flat ground and
that he got as close as he did through a combination of coincidence and cherry
picking (deciding after he knew the right answer how much the added gas
weighs, changing his estimate of how much of tire's surface consists of
grooves after he knew the right answer).

------
kyleblarson
Wasn't there a Feynman story where he did this exact same thing?

~~~
as89
That would be cool. Do you remember where you heard this? Would love to see a
source.

------
YarickR2
Well, the idea is nice, but, as others have said, we need to account for
sidewall stiffness. But we can do better with law of large numbers and
employing metering tape to measure difference in car height with different
pressure in tires. First we need to collect baseline data - tire brand, model
and size, tire pressure, and car height difference , for known car weights,
for two different pressures (say, 20 and 35 psi), this way we could deduce
tire sidewall stiffness for given make/model/size of the tire. After that we
can do the same for all cars with same tires, by measuring car height
difference between two pressure points. Measuring height changes on both axles
(wheel center to lowest point of the wheel arch) will get us weight
distribution ; but we'll need to account for staggered tire setup .

------
jcrawfordor
A related method is used commercially for self-weighing trucks. Typically it's
done by measuring change in the pressure in the suspension airbags and needs
to be calibrated for the specific suspension and airbags being used. One major
vendor lists the accuracy as +/\- 300 lbs which is pretty good for use in the
30-40 ton range but not so good for a passenger vehicle.

As a bit of cool technology trickery, the Air-Weigh system encodes the weight
data onto the existing tractor-trailer electrical connection so that the
weight can be displayed in-cab without any extra wiring to connect. They don't
say much about how but I'd guess RF modulation on the electrical for the
lights or something.

------
ummonk
The edges of the footprint won't be bearing full pressure because they will be
in tension (in fact, load distribution profiles of tires tend to look like a
rounded trapezoid).

Additionally, the grooves are rather stiff and will help hold the treads - the
air pressure on the inside of the grooves will be helping push the treads onto
the road. Likewise, tire sidewalls have some stiffness and will also be
helping hold the car up beyond just the air pressure, as you've noted in your
addendum.

This is a good heuristic for approximating the weight of a car but you won't
be getting particularly accurate weight measurements out of it.

------
s1artibartfast
The tread should not matter, because the force gets spread under the tread
groves before you reach the inner diameter. You should also consider the
thickness of the tire rubber, as this could reduce the pressurized contact
area.

------
tempestn
Another option is to measure the compression of the suspension springs and
then use the spring rates and the suspension motion ratios to calculate the
corner weights.

If course that would only give you the sprung weight, but you could jack up a
corner and then weigh just the unsprung components with a single bathroom
scale. (Subtracting any contribution from the spring, if it's still compressed
at all.) Either that or remove and weigh a wheel and then estimate the rest.

------
phibz
Can you do this purely with pressure?. Lift the car off all 4 tires then add a
known pressure to all tires, just enough to seal the beads. Then lower the car
and measure the pressures again. I'm sure you could get to the ratio of weight
distribution for your car. And with the right coefficient for your tire you
could probably accurately approximate weight.

~~~
basicplus2
if you know the exact volume of the tyres and account for any temperature
change this should be acurate

------
fouc
I've been assuming that public buses would be able to detect how many
passengers might be on board by detecting the weight changes from an internal
sensor of the tire pressures. Count the jumps up and jumps down in weight as
people step on and step off, etc.

And that they'd be reporting that back to the central database along with
their gps etc.

------
Someone
[https://en.wikipedia.org/wiki/Saab_96](https://en.wikipedia.org/wiki/Saab_96)
says “873–950 kg (1,925–2,094 lb)”. Middle of that range is 911½ kg (2,009½
lb).

Reading the comments here, that probably is more accurate than this hack. It
isn’t as educational or entertaining, though.

------
swsh
Pretty difficult to get any form of accuracy with this because you can't
easily account for tyre sidewall stiffness

~~~
nickff
How does sidewall stiffness matter? The ground is holding the car up; the air
is not.

~~~
mulmen
I can drive my car safely at 55mph with 0psi in the tires. I believe this
methodology would suggest my car is weightless in such a situation.

------
rlpb
> We want to find the force at each tire. So by rearranging, we get F = PA.
> The pressure is gotten by a tire pressure gauge.

Can someone explain why the air pressure inside the tire is the same as the
pressure that the tire applies to the ground? Ignoring sidewall stiffness as
pointed out to others, why must this be true?

~~~
yk
Because the tire would deform, if there is a net force on it. Therefore the
force from the inside is the same as the one on the outside. (However, that
argument has only any chance to hold at the contact point from the tire to the
ground, since obviously everywhere else the tire does not perform because of
stiffness of the tire material.)

------
gbtw
In the Netherlands they use driving axle load systems usually in the right
most lanes on the highway that feature trucks. There is also a service that
automatically calculates the tire pressure and sends a message to the company
if the tires are deflated when driving over these weigh points.

------
jaxx75
Assuming all tires are the same, I think this would be most applicable for
weight distribution alone, but not really for the weight. For performance
applications, distribution is most important

The author also did not ensure the ground was level, which of course would
have an effect on the weight distribution.

------
angry_octet
Maybe use a lever instead? If you have a decent length of steel pipe or 2x4
and a trolley jack. Lever one end of the trolley jack up on a pivot, you
should easily be able to get 20:1, within range of a cheap luggage scale or
convenient heavy objects. Have to do front and back of course.

------
mannykannot
There's a period, after it rains, when, as cars that have been standing in it
drive off, they leave behind a wet print of their tire contact patches. With a
jug of water and some patience, perhaps you could use this to get a more
accurate measure of the contact area?

------
kozak
By the way, a car with electric propulsion and regenerative braking should be
able to "know" its weight quite precisely (from the amount energy that is
needed to accelerate or the amount of energy that is returned when regen-
braking).

~~~
londons_explore
After you've subtracted the effect of thousands of hard to measure variables
like the slope, the tyre rolling resistance, the resistance in the wiring, the
magnetic flux saturation in the motor, the accuracy of the current sensors,
etc, etc, etc...

~~~
xchaotic
Not thousands but a few and most of them are measured anyway, like slope with
a gyro or battery drain. No need to over complicate it just measure the amount
of regen the more you get the more the car weighs.

------
mips_avatar
I got this question asked in an interview for a mechanical engineering
internship. I was asked "you are given a ruler and a parked car, how can you
measure the weight", took me about 10 panicked minutes and 4 hints before I
figured it out.

------
lkxijlewlf
Look into WIM (Weigh in Motion) and Tire Anomaly technology. I don't know how
much you'll find out on the internet about specific details, and I can't
elaborate, but it's pretty interesting.

------
guygurari
The suggestion is to use F=PA to measure the car weight, where P is the tire
pressure, A is the area the tires in contact with the ground, and F is the
unknown: the weight of the car (measured in terms of gravitational force).

I don't think this works. To see why, suppose we make the tires out of a very
stiff material. We control the pressure P, but changing the pressure will not
change the surface area A. Therefore, by changing P we can set F to whatever
we want, which shows that we are not actually measuring the weight of the car.
The basic issue here is that the air pressure is not the only thing that is
supporting the car.

I don't know how important the stiffness effect is for real tires, but I
suspect they are sufficiently stiff that it matters a lot.

~~~
tmoney1818
I think he nixes your case at the start, when he goes through the sanity check
thinking about the flat tire. Also, I think your rigid body case use the walls
of the tires to apply force to the care, not the force from the pressure to
keep the car static, which is why it fails.

~~~
guygurari
I agree that higher tire pressure results in smaller surface area, but it's
not clear to me that the tire itself does not support the car, skewing the
result. So I'm not convinced this sanity check is sufficient. For example, as
another commenter mentioned, run-flat tires can support the car on stiffness
alone.

~~~
abstrakraft
I agree, the sanity check is not sufficient. It confirms the concept that as
pressure decreases, area increases, but is not sufficient to confirm a linear
relationship. In the limit, the area clearly does not become infinite when
pressure drops to 0.

For the case you suggested above, this is essentially how run-flat tires work.
Of course, the sidewall of the tire isn't as stiff as the support ring, but
they do provide some support.

------
kokey
A slope and a crane scale could have been relatively cheap and I'm guessing
estimating the friction would be more accurate than making assumptions about
the tire wall strength.

------
davewasthere
Or just use one bathroom scale, and a lever to adjust weight of a single wheel
to within the scales limit, then measure each wheel individually and add the
results.

------
asimjalis
Random thought. Could you compare acceleration going uphill, downhill, and on
a level street to estimate mass, somehow keeping the RPM the same on the
engine?

~~~
jaxx75
You would have to know the rolling resistance of the tires, aero load, and the
exact amount of horsepower the engine is outputting to the wheels. It is
impractical, once you consider engine wear, air density, and probably a few
other factors required to get a correct reading.

------
serf
a similar was (maybe is) used by the California Highway Patrol to determine
whether or not truck drivers are carrying too heavy a load, or too heavy a
load down specific streets or highways.

my father was erroneously pulled over by a CHP that used a similar method,
taken to a weigh-scale, and was actually under-weight. Wooops!

~~~
as89
Interesting - similar meaning they measured the contact patch of the tires? Or
something else?

------
danbr
Upvoted for the Saab

~~~
aucontraire
Such a lovely vehicle!

------
sm4rk0
A genuine hacker!

------
0ld
theydidimperialmath. impressive.

------
ordx
Can moderators remove utm codes from the url?

~~~
dang
Ok. Submitted URL was [https://surjan.substack.com/p/16-weighing-a-car-with-
tire-pr...](https://surjan.substack.com/p/16-weighing-a-car-with-tire-
pressures?r=64gpc&utm_campaign=post&utm_medium=web&utm_source=hackernews).

------
aj7
Remarkably inaccurate.

This is a negative result.

