How many commas is too many commas?
By looking at our data we can see a clear pattern, or trend, in our data that, as the steepness of the inclined plane increases, the effort force needed to make the object move increases, but...
How many commas?
Instinctively you have too many, but you are using most correctly.
The comma before 'but' is only appropriate if 'but' begins an independent clause or if there is another dependent clause that you are setting off.
In your example a case can be made for all the commas (except potentially the last, and perhaps also the comma preceding 'as'), but you'd do better to rephrase so that you don't have so many nested dependent clauses.
Here's a great link for the rules.
@DPT got my biggest complaint... there are a few others I would like to point out.
a clear pattern, or trend, in our data
That was my big complaint. I would suggest that you fix the Pattern/Trend defintion thingy as both should be easily known by your intended audience. Trend is more clinical, which is what this looks like this is going for.
our data that, as the steepness
This comma is not needed. You're not separating two like or similar items here. Change to "...that as..."
TL;DR: Loose all but the second to last comma and excise the "or trend" in some way to make it fit better. Depending on what follows the "but..." you have, you're getting close to a run-on-sentance. State that you have the trend, then explain the objection being noted by the But. Two sentences.