I Knew How To Do This Back In The Day, lol

Winesalot

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Here is the real world scenario. I am going to haul an 8 foot diameter by 27 foot long water tank on my trailer. I would like to screw several 2x4's to the trailer deck o either side of centerline so that when the tank is lowered on to the trailer it will roll slightly to the exact center.

So the math question is how far from 6 o'clock (where the bottom of the tank is touching the trailer deck) will the tank be 1-1/2" off the trailer deck?
 

Subhotosh Khan

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x^2 = 48^2 - (46.5)^2

x = 11.906" (I would round down expecting the corners of the 2x4 will be squished a bit due to the weight of the tank)
 

Winesalot

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Thank you!!!

Once the tank is set I plan on stacking multiple 2x4's following the curvature of the tank and screwing each to the board below it making a roll brace I will have three of these assemblies on each side of the tank.
 

Winesalot

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Would you mind sharing a lesson with me? It's been a LONG time since I was in a scholastic environment and I don't use math other than some chemistry calculations in my winery lab. I see you used the difference in the radius to the second power and I get the basic algebra used to solve for x but I expected to se Pi in the equation
 

lev888

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Would you mind sharing a lesson with me? It's been a LONG time since I was in a scholastic environment and I don't use math other than some chemistry calculations in my winery lab. I see you used the difference in the radius to the second power and I get the basic algebra used to solve for x but I expected to se Pi in the equation
Make a drawing (what you see looking along the axis of the tank).
You should have a circle, a line for the trailer deck), a vertical line for one the 2x4s. Add a vertical radius, another radius to where the tank touches the 2x4. Add another line to make a right triangle, apply the Pythagorean theorem.
 

Subhotosh Khan

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Would you mind sharing a lesson with me? It's been a LONG time since I was in a scholastic environment and I don't use math other than some chemistry calculations in my winery lab. I see you used the difference in the radius to the second power and I get the basic algebra used to solve for x but I expected to see Pi in the equation
Draw a circle of radius 'r'.

Draw a horizontal and a vertical line through the center.

The center is your origin, the horizontal line is x-axis and vertical line is y-axis.

Every point on the circle satisfies the equation: x2 + y2 = r2 = 482..............................(1)

Draw a horizontal line parallel to the x-axis and through the point where y-axis intersects the circle. This line is your truck-bed.

Now choose point on the circle (near the truck bed), which is at a height 'h' from the truck bed.

The y-coordinate of this point is [-(r-h)]. We need to calculate the x-coordinate of this point (x1).

Since this point is on the circle - it has to satisfy the equation (1)

Then we have:

(x1)2 + [-(r-h)]2 = 482

(x1)2 + [(48-h)]2 = 482.

(x1)2 = 482 - [(48 - 1.5)]2 ....................That's it....

Now you owe me one those bottle of fine wine!!
 

Jomo

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hoosie

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hoosie

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Winesalot

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You all rock. All of this makes perfect sense and brings back memories of Navy Nuclear Power School back in 1985. For those that feel I owe them a bottle of wine (😛) I am more than happy to pay up in person when you visit our winery that will open next spring in the Lake Chelan Valley (WA).

FYI..I screwed the first layer of 2x4's to the deck of the trailer 11.75 inches from centerline at 7:30 this morning and, along with several more layers of boards, several chains, and a bunch of ratchet straps the tank made the 7 hour trip to its new home without incedent
 
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