Is 39 moves the longest a chess game can go moving only pawns?

Question

I've thought of a few different ways a chess game could go on moving only pawns, but I've only counted moves in one scenario:

1. Both White and Black take 16 moves to line their pawns at the middle of the board.
2. With a series of orderly captures in 8 moves, White and Black each wind up with 4 pawns each.
3. Taking care to threaten the rooks first, White and Black move their pawns within striking distance of the opponent's non-pawn pieces. This would take 16 moves (bringing the total up to 40), except that...
4. As soon as a White pawn threatens the Black king, Black would be forced to move the queen, a bishop or a knight to protect the king.

Have I thought through this scenario correctly? And even if I have, might could there be a scenario in which moving something other than a pawn could be put off longer?

Answer 1

Edit: This is an improved version of my previous 39-move solution (using Ross Millikan's suggestion to let the pawns advance as far as possible befrore being captured).

1. c3 b6
2. c4 b5
3. c5 b4
4. c6 b3
5. g3 e6
6. g4 e5
7. g5 e4
8. g6 e3
9. axb3 dxc6
10. fxe3 hxg6
11. h3 a6
12. h4 a5
13. h5 a4
14. h6 a3
15. h7 a2
16. hxg8N axb1N
17. b4 g5
18. b5 g4
19. b6 g3
20. b7 g2
21. bxa8N gxh1N
22. b3 g6
23. b4 g5
24. b5 g4
25. b6 g3
26. b7 g2
27. bxc8N gxf1N
28. e4 c5
29. e5 c4
30. e6 c3
31. e7 c2
32. exf8N cxd1N
33. e3 c6
34. e4 c5
35. e5 c4
36. e6 c3
37. e7 c2
38. d3 f6
39. d4 f5
40. d5 f4
41. d6 f3
42. exd8N f2+

Answer 2

You can do better by having pawns move more before being captured.

1-4   b2-b6     g7-g3
5     hg        ab
6-9   g3-g7     b6-b2
10    g7xh8N    b2xa1N
11-15 g2-g7     b7-b2
16    g7xf8N    b2xc1N
17-21 a2-a7     h7-h2
22    a7xb8N    h2xg1N
23-26 e2-e6     c7-c3
27    dc        fe
28-31 c3-c7     e6-e2
32    c7xd8N    e2xd1N
33-37 c2-c7     e7-e2
38    f2        e2xf1N
39-42 f3-f7+    d7-d3