# Pressure washing lead me to recall calculus

Discussion in 'Bad Dog Cafe' started by Chick-N-Picker, Jun 13, 2015.

1. ### Chick-N-PickerTele-Afflicted

Age:
25
Apr 26, 2015
North Carolina
Lately I've been pressure washing some houses and a few driveways. I just charge whatever and have done some for free because, well, I'm too nice. I pressure washed a 100'x30' rectangle driveway yesterday and the standard is .20-.30 per square foot for driveways. Not that I use that method. It's just standard.

I started thinking what if it was a semi-circle driveway but not actually a true half circle, so ((3.14)r^2)/2 minus the inside would not work.

I thought how in the heck could I find out the area of the drive way. When I thought if I treat the driveway as the positive quadrant of a graph I could figure it out.

These are hypothetical numbers just to show the process.

For example I could measure from end to end of the outer most edge of the driveway and let's say it's 100'. That would be 0'-100'. Now do the same for the inner most edge of the driveway and let's say it's 90'. That would be 0'-90'.

Now if I go to the center of the 100' and measure up to the tallest point of the arch and let's say it's 30'. Now do the same for the 90' and say it's 20'.

Now I know that sense the function of the graph only has one curve it's a squared function. So basically if I take the integral of the outer function and minus the integral of the inner function it should give me the area of the driveway.

So it would be integral 0'-100' of x^2+30
Minus the integral 0'-90' of x^2+20

I believe this is correct. I took advanced placement calculus in high school, which is basically college level but our teacher said it was more thorough and more difficult. I made an A+. It was my favorite math and I was just thinking the other day that I would like to take a refresher course.

2. ### AlamoDoctor of TeleocitySilver Supporter

Nov 15, 2006
Berlin
I think that was my favorite math to miss out.

3. ### String TreeDoctor of Teleocity

Dec 8, 2010
Up North
You have no choice but to charge for your estimate too!

4. ### Chick-N-PickerTele-Afflicted

Age:
25
Apr 26, 2015
North Carolina
I just imagined. What if I did this to the customer?

You'll have to show him the work!

You never know when math might help you. When my father was a student, he got a ticket for going through a stop sign that he thought was obscured by a tree and hard to see so he went to traffic court. The judge asked him what he did; my father said he was an engineering student. The judge immediately asked, what is the indefinite integral of 1/x? My father replied, "ln(x)". The judge let him off!

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6. ### dsutton24Doctor of TeleocityAd Free Member

Dec 29, 2010
Illinois
Calculate the length of the inside edge of the curve (half of what a similar circle would be), add to that number the length of the outside curve. Divide by two, then multiply by the width. You've essentially turned the semicircular driveway into a rectangle.

You could use a walk off wheel and not even have to calculate the circle segment lengths. Zero it, walk off the inner edge, without zeroing it again walk off the outside edge. Divide by two, then multiply by the width.

Easy.

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7. ### bluenote23Tele-Meister

Not that anyone is going to be too concerned but I don't think your integral would work.

You're dealing with a parabola, X^2 = 4pY where p is the focus. So you would need to base your integral on this. Of course, you're missing an important number here.

Another way to approximate the area would be to make a parallelogram. So in your example you would have a rectangle 90 x 10 and two 25 sq. ft triangles. This would be approximate at best though.

8. ### Larry FDoctor of TeleocityVendor Member

Nov 5, 2006
Iowa City, IA
My dad was a very smart guy, getting a full scholarship offer to MIT, which he declined because "I wanted to work." He wound up at Hanford Engineering Works, working on reactors that made plutonium throughout the Cold War. Water flow is a major issue in reactors, so he spent much of his time there dealing with flow calculation.

When the reactors began closing, he started his own business working with municipal water treatment plants on the west coast. Whenever someone was watching him work, he would bring out his slide rule for the calculations, even though he had already done the math in his head.

Back at Hanford, the workers' radiation exposure was monitored. When they reached their monthly limit (a very problematic concept then, as now), they were not allowed to enter certain areas. The guys in my dad's group would use their restricted time to invent little atomic widgets, play pranks with radiation, and share shortcuts for calculating numbers. I think these would fall under the heading of what is called today, "recreational mathematics."

Well-meaning as he was, my dad's tricks messed me up by the time I got into algebra and set theory.

I was working on a music PhD at the University of Chicago, which had a killer math faculty, one of whom was my second thesis reader. My paper used a lot of group theory, which is commonly expressed with letters, rather than numbers. At the conclusion of a meeting one day, he told me that he could next meet on, say, Tuesday, after he finished a class at 10:30. "Let's meet here at 10 minutes after that, whatever time that is."

This reminds me of the old saying of mathematicians that such-and-such a problem "isn't mathematics, it's arithmetic."

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9. ### bparnell57Poster Extraordinaire

Feb 10, 2014

I like this method much more, as it is much more likely that the width is a constant rather than the curve following a function. Also, if it's a constant radius curve, but ends at an angle that isn't perpendicular to the curb/street, then you may determine the arc length in degrees, divide this by 360 in order to get your multiplier, and find the area of a complete donut of driveway (you'd have to calculate the radius using perpendicular measurements from the outer edge to a meeting point (chalk rope anyone). Multiply the donut area by your multiplier and you have a good estimate for the area of the donut bite.

10. ### Nick JDDoctor of TeleocityAd Free Member

May 12, 2007
Queensland, Australia
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11. ### Westerly SunnPoster Extraordinaire

Jul 28, 2006
S.E. North Carolina
I would step off the driveway right down the center and treat it as if it were straight.

Aug 22, 2004
New York
It's hard to tell true shape of the driveway from the picture because of the point of view. If the curves are really circular, you don't need calculus to find the area of the driveway. The calculus has already been done when you use the formula pi *r^2 for the area of circle.

13. ### ObsessedDoctor of TeleocityAd Free Member

Nov 21, 2012
Montana
You could use the Taylor Series technique and be close enough. Or to double check yourself.

14. ### Chick-N-PickerTele-Afflicted

Age:
25
Apr 26, 2015
North Carolina

The driveway in the picture is just an example of the type of driveway I was speaking of.

And I pointed out that if it was a perfect half circle and I knew it was then I would use that formula.

15. ### JackStrawFriend of Leo's

Mar 22, 2008
In The Pines

Why are you pressure washing driveways? Seems like an incredible waste of potable water if that's what you are using. Not busting on you and no malice intended just don't like to see water wasted when so many go without.

16. ### Chick-N-PickerTele-Afflicted

Age:
25
Apr 26, 2015
North Carolina
This is the short answer. I did type a long answer but decided to erase it.

Because people want their driveways cleaned and they make pressure washers to wash things that otherwised couldn't be cleaned. My area is not in a drought.

17. ### Mike EskimoDoctor of TeleocityAd Free Member

Nov 9, 2008
Detroit
I mean technically there could be a water recovery/reuse system but I have no idea how it could work economically.

We're in no drought either Chick-N-Picker and I use buckets and buckets and buckets of water per day - because folks pay me to as well.

Wish you were up here - I'd have you do my big concrete porch prior to me re-staining it.

And I'd pay you !

18. ### Chick-N-PickerTele-Afflicted

Age:
25
Apr 26, 2015
North Carolina
I'll be there Monday morning at 8. So with labor and gas it shouldn't run more than \$1000 haha.

And I know your not in a drought. It's raining out the NASCAR race today. Maybe it will move on out and they can race.

19. ### dsutton24Doctor of TeleocityAd Free Member

Dec 29, 2010
Illinois
Way to bring down a fun thread! Pressure washing is pretty efficient water-wise. The water used isn't contaminated in such a way as to cause trouble with streams and the water table, and the sun recycles it for free.

Maybe we should worry about wasting electrons when so many go without?