I've been trying to find a reputable source for the cause of this but I'm having little luck.  There seems to be a well known idea that running an engine with just open headers or just a collector with no long exhaust will eventually "burn the valves."  The idea is that they warp and then lose enough contact with the head for heat dissipation.  I've also seen people saying that exhaust leaks can do this also.  The theory is that upon shutdown, cold air can reach the valves and warp them especially if they are open (unseated from the head).  One counterpoint to this theory is that losing an exhaust causes the engine to run lean, and this is what actually causes damage to the exhaust valves.  Does anyone know the truth behind this?

Also, during the valve overlap portion of the combustion cycle, isn't a fresh dose of cold air hitting the exhaust valve anyway?

spectreeng;  It has been my experience that those engines being run with open headers, are being run without an eye to ultimate longevity. i.e., they generally are race engines.  That being observed, do race engines burn exhaust valves more often than non-race engines?  Certainly.  However, if engine longevity is a key consideration for a particular race engine, then many factors come into play, which may effect total exhaust valve life life:  Valve seat width.  A/F ratios.  Camshaft timing. (Including intake to exhaust overlap, and centrelines.) Header tuned length. Header primary diameter, Valve materials. Ect.  This a loaded topic, not easily condensed into one response.  I'm sure others can give you the advice you are looking for, in much more detail.  I for one however remain skeptical that convection of cold air up the header will cause the valves to warp.

The problem as I've heard it described is that momentary flow reversals expose the valves(Forged Steel Valves) to cold ambient air on the backside, or at least to high temperature differential. If that's the real failure mechanism, a very short exhaust - probably only a few inches - would be sufficient to prevent this. I've never actually seen a failure definitively attributable to this despite seeing engines operating in many conditions that could theoretically trigger the problem.

This is a very generalised question with a huge amount of variables.

To fix issues we have to find the CAUSE of the problems, after some thought i see it may be quite possible to OVERHEAT the exhaust valves with open headers without a collector being used, depending on the state of tune of the engine itself.
Performance n/a engines without the collector are not going to Scavange worth a Damn.
So in fact maybe the Cause is the LACK of cooling doing the damage & not being cooled to quickly as mentioned.
With increasing Temperature rise at the exhaust valve from the Lack of cooling with NO scavanging to aid the issue.

With a collector i can't see this happening unless the collector is of poor design & not suited to the application.

As already talked about is the metalurgy of the valves themselves, not to mention the amount of modifications one can do to the backside of the valves to increase flow or hinder reversion which in some cases can & will reduce the life of valves.
I myself in an attempt to make components as light as possible or to configure flow or to take anti reversion measures to the next level have fallen victim to my share of Burnt, Warped & Bent valves for various reasons.
This has never happened when tuning or playing with exhausts though..

Running high spring pressures with highly modified or CHEAP valves is a good source of Warped valves & a starting point for burning valves.

Another source of "ultra lightweight" valve warping has been NOT using Torque plates for the valve seat cutting operation. Heavier unmodified valves seem to retain there shape better than valves with less material to support them.

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