just a thought is it at all possible that maybe it was at one time slightly deeper & ergo less wide & has shape changed over time & become flattened due to moisture/shrinkage...? or if it had originally been shaped/molded pressed clamped when wet and left to dry in new shape... sounds improbable but....
Here is a wee cut & paste that might make me sound a little less mad...
Before we go into the different methods of straightening, non-intrusive and more intrusive, let's ask ourselves: what is wood? It is a sponge like material made of cells and fibres that swell and shrink depending on the temperature and moisture in the surrounding air, although to different extents in different directions.
When a tree is felled, first of all the water in between the cells evaporates, then shrinkage sets in as some of the water within cells dries out. Drying from its green condition, wood will retain its original dimensions until the moisture content falls to about 30%, from which point it will shrink as it dries. The moisture content is expressed as a percentage of the dry weight of the wood: a piece which is half dry wood fibre and half moisture will therefore have a moisture content of 100%. A certain percentage of bound water (that is the water within the cells) always remains. With thorough air-seasoning, the moisture content of most types of wood will fall to between 23 and 17%, at which level it will be in balance with the moisture content of the air around it, and would, in those pre-central heating days, be stable enough to be made into furniture.
In your careers as restorers you may have noticed that much antique oak furniture has not suffered from warping as much as other timbers, whilst mahogany furniture for example seems to have more than its fair share of such problems. The principal reason for this is that much of the wood used for oak furniture was quatersawn, so that the width of the board followed the radius of the log along the medullary rays, at right angles to the annual rings. This cut produces a board which is still liable to shrink but not distort. This popular cut has a name: it is called wainscot after the Dutch word 'wagenschot' and another reason for its popularity is that the medullary rays show quite attractively. There are several explanations for this name; the most believable one is that a 'wagenschot' is the shaft that connects the horsespan of a chariot or 'wagen' with the moving axis between the front wheels. It is evident that this shaft had to be extremely strong. Therefore the wood was riven rather than sawn, producing a piece with the longest grain possible.
When a panel was made from such quartersawn or wainscot boards, it would be fitted in a rebate frame without glue so that with seasonal environmental changes it could move freely. If such a panel has split, it is probably because movement has been inhibited by accumulations of dust and grit.
In the case of mahogany furniture, it seems that there was a demand for the widest board possible, which often meant taking a piece from the full thickness of the log. Such a board was cut through the growth rings of a tree at varying angles across the width, therefore exposing it to problems of distortion. Maximum shrinkage takes place at right angles to the radius, so while the quartersawn board loses a bit of its thickness, a tangentially cut board will tend to warp. Sapwood dries faster and shrinks more than heartwood. Easy to remember, it is obvious that the annual rings tend to straighten in this process.
A cool environment with a relative humidity of about 55% and a little bit of air movement (draught) is said to be ideal for wood and antique objects in general. Your customers want to be informed about this. Also advise them to turn up their thermostats gradually as autumn approaches and lower the setting step-by-step when spring comes. A sudden change in the circumstances is the worst thing possible as the moisture will be sucked out of or pushed into the material far too quickly causing even more tension inside it.
