A lot of people have opinions on Heavy Bottom Caps! But what is the truth? How does science explain what we experience when adding inertia to the bottom of the valve casing? It just so happens that I have invested a fair amount of time, energy, and money finding the answers to these questions. The results are not surprising to some, but unbelievable to others. Today, I'll share with you the psychology behind this controversial subject.
First, let's define a few things. Inertia is the subject of today's discussion so we'll start there. By searching for the definition of "Inertia" on google, I get the following:
a property of matter by which it continues in its existing state of rest or uniform motion in a straight line, unless that state is changed by an external force. "the power required to overcome friction and the inertia of the moving parts"
This definition is quite vague so let's move to the definition of Inertia according to Isaac Newton's first law:
Newton’s first law states that if a body is at rest or moving at a constant speed in a straight line, it will remain at rest or keep moving in a straight line at constant speed unless it is acted upon by a force. In fact, in classical Newtonian mechanics, there is no important distinction between rest and uniform motion in a straight line; they may be regarded as the same state of motion seen by different observers, one moving at the same velocity as the particle and the other moving at constant velocity with respect to the particle. This postulate is known as the law of inertia.
We will use this basic definition as it gives us enough parameters to apply to the inertia value within an acoustic brass musical instrument. There really is more to it, but the basics will be more than enough to get us started.
So what happens when you add an ounce of brass (or any other material) to the bottom of your valve casing? If it is secured tightly (usually with threads), this added mass increases the inertia of the valve casing. And the added inertia reduces the amount of standing wave energy that is transferred into vibration energy. This results in increased standing wave energy to the bell, which increases resonance and amplification. In general, stability of some notes will be improved both on attack and sustain, potential for dynamic range increases, and potential for achieving the natural overtone series of the entire closed system increases.
What does that mean? It will be easier to play the note. It will be easier to hold the note. The note will be closer to the tone color as defined by the tapers and linear relation to air volume within the oral cavity, mouthpiece, leadpipe, and bell.
When I refer to the "note", I'm using a generalization to describe any pitch or pitches affected by the added inertia and resulting added resonance within instrument specific to the location of the anti-nodal high pressure zones within the tubing, pistons, valve casings, etc. This anti-nodal high pressure is present on every pitch beginning with the fundamental and increases in number as we move up to each higher partial. The fundamental creates one anti-node in the center (linear length) of the instrument. The next partial creates two anti-nodes, equally spaced between the nodes, which are the ends of each wave form. The second partial creates three equally spaced anti-nodes and so on.
Any note that creates an anti-node near thin material tubing or features may set that material into vibration if the energy is sufficient to overcome the inertia in that area. Since higher partials have more anti-nodes, we have ever-increasing potential for material vibration as we play higher notes. By adding inertia, in the form of mass or some other mechanical design, the transfer of energy at anti-nodes can be reduced or completely eliminated.
Harrelson trumpets were designed and engineered from the ground up to solve the low inertia problem. And heavy bottom caps existed over one hundred years before I was born. Someone understood and applied this theory long before my great great grandparents were alive. I simply rediscovered the basic theory of inertia and how it pertains to resonating musical instruments in 1992. This is not something I invented nor do I take any credit for the theory. But I have invested nearly 30 years into the application of this theory to achieve MBR, which is Maximum Bell Resonance.
Hopefully, this explanation opens your eyes to the physics side of "heavy bottom caps" and maybe even gives you a glimpse into what is possible. Imagine a trumpet where anti-nodal high pressure zones have no affect on the energy potential of the standing wave and the bell resonates at its full potential. What would the world be like if we were all playing instruments that expressed every bit of energy we so lovingly put into them?
Here's a video diving deeper into this subject...