Removing slight bow from middle of board

[Hurricane Dry]

So I had this old couch that wasn't worth reupholstering.  It's a little over 20 years old and I saved the bits of wood the frame was made out of.  The manufacturer appeared to have used lots of cut-offs from other furniture making processes, so I have some a mixture of red oak, white oak, and I believe walnut sap wood.

I have been practicing hand planing on these pieces.

I have LN #4 smoother (bevel down), LN #5 Low Angle bevel up Jack, and LN low angle bevel up rabbet block.  I have gotten to the point where I can sharpen all three blades very well and all three planes can cut very good shavings.

I will probably buy a #5 or #7 bevel down plane in the future as for most work I prefer the bevel downs.

I am able to produce reasonably flat and square surfaces.

But there is one thing that escaped me.  I can't get that last little bit of bow out of a board.  I don't have a good vice or a good work table that holds the work very well,  This doesn't stop me from getting the edge square or the face mostly flat.   I'm using an MFT table that is mounted to a very sturdy cart.  It does not shake, but my method of trying to duplicate a dog vice is not very good.

What happens is I have good success working the high part of the bow on one side of the work and the pointed down parts of the other side.  I get the part pretty flat on both sides (parts are slightly longer  than 24 inches).  But then the plane seems to stop cutting the high part of the bow.  It's like the bow flexes down and then the plane won't get to the high.  I have tried switch back between the #4 and #5 but still get similar results.  The grain is such that the #4 seems to work better in most cases.  I can turn the plane and cut across the board to try to knock down the high, but I still trouble taking the last bit of bow out.

Anybody have any tricks or advise? 

[Tpt life]

Shim the curve so it won't push down or flip it over and plane the ends. 

[Tom King]

Hold the plane in one plane so it doesn't take wood off the lower edges.

 

[Hurricane Dry]

1 hour ago, C Shaffer said:

Shim the curve so it won't push down or flip it over and plane the ends. 

Thanks.  I did the shim.  It worked.  i kept moving the shim around to better hit the high.

I had tried taking the end highs down on the other side, but that didn't help as still get too much movement with my sorry power tool style clamping set-up.

I will build a proper bench, but I have been making melamine or plywood shop cabinets, so I don't have a major need as of yet.