My method used before is mildly inaccurate but didn't involve to much thought on my part to start with (and gets a "close enough" answer). The correct solution is actually a bit easier, but I had to go look it up
.
This link pretty nicely describes the difference between a class 1 (what you're thinking of: fulcrum in the middle) and class 3 (what I was thinking of: fulcrum on the end opposite the load) lever and the relative distance advantages between them clearer than I can. The short version is that putting the fulcrum on the end of the lever (class 3) gives you significantly more lift for a given length of lever arm than a class 1.
https://www.school-for-champions.com/machines/levers_increase_distance.htm#.WonEfIKIbBI
So taking their formula:
DO/dO = DI/dI
We have multiple "knowns"
D0=36 - this is the lifting height, you have a constant goal of 36
D1=24 - the capacity of your jack which also constant at 24"
d0=48 - some assumed maximum length of the lever arm (we have to make something up for this)
So we can plug that in and get:
36/48 = 24/? which is 0.75 = 24/? which is 0.75 * 24 which is 18.0"
pre-doing the algebra that's d1 = D0/d0 * D1
which is: 36/?load arm length? * 24 so you can just plug in different load arm lengths and get an answer for the offset with that.
Thus for a class 1 lever you would need a total lever length of 66" (load arm of 48" plus effort arm of 18") with the fulcrum 18" from the jack to lift the load end 36". I could re-jigger the formula to get the total lever length but just plugging in a set of possible numbers is fast enough here.
For a class 3 lever you would need a total lever length of 48" (load arm of 48") with the jack 18" in from the fulcrum end to lift the load end 36".
The advantages of a 3rd class lever for this use case become reasonably apparent here. This isn't accounting for any problems of practicality in having angles that steep, that will depend on what you have for pivots, etc.. Note also that the ends of the load and effort arms describe an arc, so that will have to be accounted for in the design (the easiest way is probably to allow the fulcrum to pivot somewhat as well as both ends of the jack - that way you can have the lift go more or less straight up and down which will be easier to stabilize on a track or something).
Visually diagramming the two example cases for a class 1 and class 3 lever.
Pre-calculating for some set of possible load arm lengths.. Remember that for a class 1 lever the total lever length is the load arm plus the effort arm but for a class 3 the effort arm is "inside" the load arm (so the load arm is the total lever length). Some of these (especially towards the short and long ends..) are likely infeasible due to the angles involved.
load arm | effort arm |
36 | 24.0 |
37 | 23.35 |
38 | 22.74 |
39 | 22.15 |
40 | 21.6 |
41 | 21.07 |
42 | 20.57 |
43 | 20.09 |
44 | 19.64 |
45 | 19.2 |
46 | 18.78 |
47 | 18.38 |
48 | 18.0 |
49 | 17.63 |
50 | 17.28 |
51 | 16.94 |
52 | 16.62 |
53 | 16.3 |
54 | 16.0 |
55 | 15.71 |
56 | 15.43 |
57 | 15.16 |
58 | 14.9 |
59 | 14.64 |
60 | 14.4 |
61 | 14.16 |
62 | 13.94 |
63 | 13.71 |
64 | 13.5 |
65 | 13.29 |
66 | 13.09 |
67 | 12.9 |
68 | 12.71 |
69 | 12.52 |
70 | 12.34 |
71 | 12.17 |
72 | 12.0 |
73 | 11.84 |
74 | 11.68 |
75 | 11.52 |
76 | 11.37 |
77 | 11.22 |
78 | 11.08 |
79 | 10.94 |
80 | 10.8 |
81 | 10.67 |
82 | 10.54 |
83 | 10.41 |
84 | 10.29 |
85 | 10.16 |
86 | 10.05 |
87 | 9.93 |
88 | 9.82 |
89 | 9.71 |
90 | 9.6 |
91 | 9.49 |
92 | 9.39 |
93 | 9.29 |
94 | 9.19 |
95 | 9.09 |