Hi,
I agree with everyone elses' info and wanted to toss out some additional.
Yes, a cast metal manifold was what originally came on the car and yours has been replaced with a tubular header, probably as a performance upgrade (possibly as a less expensive replacement, if the original manifold were damaged in some way).
The original cast Triumph manifolds aren't all that bad in terms of performance. There are a few places where they can crack/break and studs in them often get rusty and/or "rust welded" in place. Or, like most studs, seems the nuts weld themselves on and the stud unthreads itself.
A thicker, cast manifold does keep more of the exhaust heat (and noise) inside it, but is also heavier and not as easily "tuned" for improved performance.
Tubular headers tend to be a bit noisier and allow more heat to pass through the thinner metal walls. On a positive note, most Triumph engines can benefit from any improved scavanging of exhaust out of the cylinders, and a tubular header is one thing that can help that. A header alone added to an engine might make a few more horsepower. In combination with other improvements, it can be more highly effective. Some other modifications (such as adding a set of Weber sidedraft DCOE carbs) practically require a header be installed to realy work well.
Tubular headers can be "tuned" to improve performance in specific areas of the engine's rpm range. This is done by using different inside diameter and length of piping, keeping the runs as straight as possible and modifying te overall design of the header. It so happens you have a "long primary" header there, with the pipes coming off the exhaust ports each being continuous all the way down to the larger "collector" at the end. This is a 6-into-1 design and was (is?) the most common type available and over the years. Probably most were installed by folks "improving" their cars and wanting "a header", without much careful thought as to what different designs can do in terms of performance.
However, basically speaking, the longer the primary pipes, the more the header is tuned for high rpms. So, while a long primary header like on yours will usually give the most increase in horsepower, it does so at the very top of the rpm range and often at some expense to torque and performance in low- to mid-rpm ranges that are actually what are much more frequently used on the street (and in some types of racing, i.e. autocross). This is not to say you must run out and change it, just that it's probably not the most ideal design for a street car. These long-primary designs are most likely copies of extensive work that's been done to develop very high performance, full race engines, by folks like Kas Kastner in the 60s and 70s and Greg Solow right up to today. They (and many others) run lots of careful dyno tests to see what works best in a specific application. However this is usually road racing, occasionally drag racing, all high rpom stuff and not very applicable to street use. (An interesting exception: The Sebring TR4s Kastner prepped used a Y-type custom header with shorter primaries, he says for more flexible engine performance in that endurance race.)
If you want to continue using a header and ever find yourself looking for a replacement, for street driving a 6-into-3-into-1 design (sometimes called a "Tri-Y") might be a little better choice. Also, consider the way any headers you look at are actually made: All bends should be smooth and not "crushed" on the inside radius when they are bent(i.e., mandrel bent) . Ideally the primary tubes should all be close to the same length. And, sharp bends nearest the cylinder head are best avoided (straighter is better) if at all possible.
Another point, the heat given off by headers increases underhood temps and, worse, on many cars including Triumphs it's concentrated right under the carbs and next to the alternator and starter. An engine works better with cooler fuel, not "warmed up" in the carb float bowls by the exhaust system! The alternator and starter will live longer if not regularly "toasted" by a lot of radiant heat.
There are several methods of dealing with this heat, which can be combined or used individually. Some "solutions" can be used with either cast manifolds or tubular headers, however heat reduction is more likely to be needed with headers becasue of their greater heat transfer.
One method is to install a heat shield (or shields). It's simply a bent piece of metal sheeting that's bolted on somehow, in between the header and whatever the shield is protecting. The idea is simply to reflect radiant heat. The most effective heat shielding has a secondary layer applied, perhaps a reflective foil and some sort of insulation in between. (Dynamat is one manufacturer of this sort of thing.)
Some other heat control methods include either ceramic coating or wrapping the header pipes themselves. A heat shield can only help reflect radiant heat, while wrap or ceramic coating will also work to reduce overall ambient temps in the engine compartment.
The header you've got is made of mild steel (the surface rust on it makes that obvious). This type of steel header is *not* generally recommended to be wrapped (a special high temp cloth tape is wound around the pipes). The reason is that the wrap greatly increases temps held within the piping (which also has a benefit of increasing gas speed, which is good for scavanging). The temps of wrapped exhaust piping generally exceed mild steel's capabilities and the metal will deteriorate quickly, shortening the life of the header dramatically.
If the header you've got there is sound, i.e. not rusted through anywhere, still has strong welds and no cracks or significant dents, you might want to send it off to be ceramic coated. This can really spruce up the appearance of an old header that's got surface rust, makes it look like new, but more importantly also acts to keep heat inside the headers and lower temperatures throughout the engine compartment. In most cases, the special ceramic is also applied inside the piping, which has another benefit that it smooths the surfaces out and improves gas flow through the header. Last time I checked, ceramic coating cost around $150 to have done. (It's best if a set of new headers is carefully fitted to the car, before coating.) There used to be only one or two places that did this sort of work, but others have popped up in recent years and you might even find a local source.
Stainless steel headers are more durable than mild steel and can tolerate higher temperatures, but are more expensive because the material is more expensive to start with, plus is more difficult to work with and weld. However, stainless steel exhaust piping will hold up almost indefinitely and can easily handle being wrapped.
I haven't made any sort of direct and scientific comparison of wrapping vs ceramic coating, but suspect the wrapping might be slightly more effective in most cases. On the other hand, wrapping will likely need to be redone every few years, while ceramic coating is relatively permanent.
Any new exhaust header you buy, if you go that route, will most likely need some hand-fitting to insure that the flange seals well and there are no stresses or strains on the rest of the exhaust system (possible exception: a good straight original cast manifold). Many folks assume they can simply bolt a header right up and drive away. Sometimes that works, other times they have to replace blown gaskets frequently and wonder why. The reason is that headers are handmade and have a lot of welding done on them. Often there is a slight bit of warpage or misalignment that needs to be corrected. The last set I fitted, Falcon stainless steel (short primary or Y-type), needed a bit of work around the mounting holes for best fit, but seemed to have a good, straight flange.
Nearly always, both headers and even the original cast manifolds can benefit from some "port matching" work, too, although that's sort of the icing on the cake during performance tuning. The extent that most people do is just fit/check that the new exhaust manifold gaskets are well fitted and aren't intruding on the ports in any way.
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