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Are these relatively recent "sport ramps":

enter image description here https://www.bricklink.com/v2/catalog/catalogitem.page?P=75538

compatible with these older "sport ramps" https://www.bricklink.com/v2/catalog/catalogitem.page?P=43086 enter image description here https://www.bricklink.com/v2/catalog/catalogitem.page?P=43085

and these corner pieces ? https://www.bricklink.com/v2/catalog/catalogitem.page?P=43086 enter image description here

With "compatible" I mean the concave sides can be aligned by an integral number of modules or plates and the circles describing the shape have the same radii. I would also be interested in what the actual radii for the elements are.

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I've put those two parts side by side in LeoCAD, and it's quite obvious they have different shapes:

Ramps, side by side

A side view illustrates the difference even more clearly:

Ramps, side view

They will somewhat align if one of the ramps is rotated exactly eleven degrees, like in the following diagram:

Ramps, side view, rotated

Do note that while it's easy to align bricks at increments of 15 degrees with hinge parts (and a few other amounts by resting over sloped bricks), eleven degrees is a hard angle to achieve.

As user @SanderDeDycker pointed out, it's also possible to align the ramps without rotating them, with a vertical offset of slightly less than 2 plates, and a horizontal offset of about 2.3 studs - again, dimensions that are hard to achieve:

Ramps, side view, offset

Applying a bit more CAD, I estimate the radius of the slope to be 11½ studs. Note how, in the following diagram, the left tangent line crosses the last stud of the grey ramp; and that the grey ramp is 12 studs deep.

CAD diagram of the radius of the slope

A bit more fiddling with CAD tells me that the "new" ramps (75538) have a slope radius of 12 studs instead.

Please keep in mind that my measurements are based on the LDraw models, and I have spent very little time on them, so they might not accurately reflect the dimensions of physical bricks.

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    I did similar measurements earlier today (with Studio models), and came to the same conclusion that the radii for both parts are very close, but not quite the same (assuming the models are accurate). The only way to match them up horizontally, would be to raise the 75538 ramp by just under 2 plates, and offset it by around 2.3 studs (see i.stack.imgur.com/sgf7Q.png) - none of which works out with lego math unfortunately. Mar 22, 2023 at 21:13
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    @SanderDeDycker Thanks for that research! I've taken the liberty of adding your stud.io screenshot to my answer. Mar 22, 2023 at 22:08

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