Quick graph that shows the equation in relation to mass ratio.
https://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation#/media/File:Tsiolkovsky_rocket_equation.svg
On Tue, Sep 6, 2016 at 11:57 AM, William Claybaugh <wclaybaugh2@xxxxxxxxx>
wrote:
Norm:
I have *always* understood logarithms to be properly called exponential
functions and their curves to be exponential curves. I am sorry that you
are confused by that and I am happy to take the lesson that you insist upon
a more exacting definition.
Bill
On Tue, Sep 6, 2016 at 11:42 AM, Norman Yarvin <yarvin@xxxxxxxxxxxx>
wrote:
This isn't about academic pedantry, but about having language be
meaningful. In some contexts it is reasonable to lump together
exponentials and logarithms, but to call a logarithmic effect an
"exponential effect" would strip the phrase "exponential effect" of
all of its usefulness. In engineering, I've often seen people use the
phrase "exponential effect" or "exponential growth" for an effect that
is merely polynomial, not exponential: growth as x^2 or x^3, not as
e^x. That's a mild abuse of the phrase; using it for growth as log(x)
would wreck it entirely.
You aren't by any chance just embarrassed by getting backwards the
most basic equation in the business, and seeking to dart away under a
cloud of ink? I mean, your original message did say that mass
fraction had an "exponential effect" while Isp was "merely linear".
That this meant the latter was less important also seems to be how
others read your message.
Now, when one effect is linear and another logarithmic, it can still
be the case that it's more cost-effective to improve performance via
the latter effect; and this can easily apply in the case of Isp, which
is often exceedingly difficult to improve. But the costs don't change
the rocket equation, and it's worth getting the rocket equation right.
On Mon, Sep 05, 2016 at 08:49:58PM -0400, William Claybaugh wrote:
Norman:more
When I was taught the exponential functions I was taught that the inverse
exponential was a part of that class. That is, logarithmic functions are
correctly generally referred to as "exponential" or--perhaps somewhat
accurately--as "inverse exponentials".are
I deduce that you disagree and instead think that logarithmic functions
not part of the class of exponential functions.
That is not my understanding.
Bill
On Monday, September 5, 2016, Norman Yarvin <yarvin@xxxxxxxxxxxx> wrote:
On Mon, Sep 05, 2016 at 07:10:08AM -0400, William Claybaugh wrote:
Norm:
A logarithm is an exponential function.
Not when you're talking about an "exponential effect", it isn't. An
exponential effect is a big effect that grows strongly as you increase
the factor in question; a logarithmic effect is a wimpy one that gets
ever-wimpier as the factor in question increases. In particular,
here, a 10% increase in Isp buys you a 10% increase in delta-v,
whereas a 10% increase in m_initial/m_final buys you less, at least
for launcher-like values of that ratio. (If, say, it starts out as
10, a 10% increase buys you about 4% more delta-v; or if it starts out
as 5, a 10% increase buys you 5.6% more delta-v.)
