Me-262, NOT Bell X-1 Broke SB First

"Tarver Engineering" wrote in message
...

"Ed Rasimus" wrote in message
...
On Wed, 8 Oct 2003 08:00:01 -0700, "Tarver Engineering"
wrote:

"Ed Rasimus" wrote in message
As I recall, the first integral of velocity is acceleration.

Nope.


Ahh, now I see. Thanks for that typically helpful addition to the
thread. Enlightenment can come in such small and pithy comments.

I hate to say it Ed but for once Tarver is right. The first *differential*
of velocity is acceleration. The first integral would be distance covered. I
understood perfectly what you meant though and envy you that experience.

Integral A dt = V0 + At =V


I've no idea what he means by this though!

John

"John Mullen" wrote in message
...
"Tarver Engineering" wrote in message
...

"Ed Rasimus" wrote in message
...
On Wed, 8 Oct 2003 08:00:01 -0700, "Tarver Engineering"
wrote:

"Ed Rasimus" wrote in message
As I recall, the first integral of velocity is acceleration.

Nope.


Ahh, now I see. Thanks for that typically helpful addition to the
thread. Enlightenment can come in such small and pithy comments.

I hate to say it Ed but for once Tarver is right. The first *differential*
of velocity is acceleration. The first integral would be distance covered.
I
understood perfectly what you meant though and envy you that experience.

Integral A dt = V0 + At =V


I've no idea what he means by this though!

It is the integral form of one of Newton's laws.

Actually, the Streak Eagle didn't ever fly vertically for more than a
transition. The profile, as I remember (the x's are numbers I don't
remember), was to takeoff, do an Immelman at IAS x, accelerate in level
flight to Mach x, then pull to a zoom at x degrees (or maybe at an angle
attack).

This was indeed the profile for the higher records: 25K and 30K (35K too?)
meters. IIRC, the intermediates (around 12-15K) were accomplished more or
less straight up.

Each profile (I think they started at 3K meters ... roughly 10,000 feet)
was approached as a separate problem. Fuel required was calculated and the
aircraft was held in position in full A/B with an pyro-release fitting. Hit
the magic fuel number and away you go. Airborne and clean up with level
accel to optimum airspeed and then do a programmed pull up to optimum climb
angle.

The higher altitudes required a target mach number before pulling up for the
zoom to altitude (approximately 60 degrees nose up_). A/B's blow out in the
65K range. Engine shut-down is a function of minimum fuel flow (The J-79
overtemped in the low 70's ... don't have a clue for the F-101) but done
shortly thereafter. It's dark up there.

R / John

On Wed, 8 Oct 2003 18:58:04 +0100, "John Mullen" wrote:

"Tarver Engineering" wrote in message
...

"Ed Rasimus" wrote in message
As I recall, the first integral of velocity is acceleration.

Nope.

I hate to say it Ed but for once Tarver is right. The first *differential*
of velocity is acceleration. The first integral would be distance covered. I
understood perfectly what you meant though and envy you that experience.

Well, the disclaimer at the beginning of my post should cover me. I
knew that the relationship between velocity, acceleration and rate of
change of acceleration went one way or the other. It was either the
first and second integral or the first and second differential. It was
differential equations at the end of my fourth semester as a chemistry
major, coupled with semi-micro qualitative analysis and physical
chemistry, that led me to see the futility of ever succeeding with the
pocket protector crowd.

I changed major to political science with the singular goal of gaining
a degree in "anything" so that I could get on with entering the AF and
flying jets.

If we change the "integral" to "differential" I'm sure that John will
recognize and acknowledge my point about aircraft accelerating through
the mach vertically.

"Ed Rasimus" wrote in message
...
On Wed, 8 Oct 2003 18:58:04 +0100, "John Mullen" wrote:

"Tarver Engineering" wrote in message
...

"Ed Rasimus" wrote in message
As I recall, the first integral of velocity is acceleration.

Nope.

I hate to say it Ed but for once Tarver is right. The first
*differential*
of velocity is acceleration. The first integral would be distance
covered. I
understood perfectly what you meant though and envy you that experience.

Well, the disclaimer at the beginning of my post should cover me. I
knew that the relationship between velocity, acceleration and rate of
change of acceleration went one way or the other.

It goes both ways:

Integral a dt = V + V0
dV/dt = a

But of course, Ed knows his airplane operating.

SNIP:
Ed Rasimus wrote:
Now, let's put to bed this idea of accelerating through the mach
straight up.
A couple reminders:
1) with a thrust to weight atio of 1.6:1 the Streak Eagle is
distinctly higher powered than anything any of us flew in the service.
2) It's shedding weight in full afterburner during the takeoff and
climb. I don't know what the fuel consumption of an F15 full-out is
but it's certainly over a ton a minute, so the T/W is increasing.
3) The only comparision I have experience with is the F104B on an AB
go-around at the end of a mission but with 1500 pounds of fuel reaming
a B model with 2 AIM9s weight about 16300. With 18000 pounds of thrust
it was very sprightly indeed. Thing was, that 18000 pounds of thrust
is measured in static condions. I have seen the fuel flow gauge on
both the F104s and the F4s rise from about 8500pph (per engine) on
pre-takeoff run up to 12000pph at 600 KIAS on level acceleration after
takeoff, obviously due to ram effect. Since jet thrust has a linear
relation of fuel burn - the thrust to weight ratio in flight cannot be
determined from thrust developed while sitting still on the ground.
Note that I do not know what is happening in the afterburner; the only
correlation I ever heard of was the AB fuel flow was about 4 times
that of the fuel flow to the engine itself. Also, the J79 manual
figure in AB for takeoff was 750 pounds per minute - per engine. FWIW
the engine fuel flow is determined by the necessity of keeping the
total air flow/fuel flow ratio right around 55 to 1. ( Lots more air
than stoichiometric needs to keep the engine from melting.)
4) So what I'm saying is that there is no doubt in my mind that a
lightened F15 with a minimum mission required fuel load could and did
exceed Mach 1 climbing vertically.
5) BTW with Jeff Ethell's flying experience and the highly visible
attitude direction indicator in an F15 why question his statement that
they were indeed vertical? Checking a vertical climb on the gyro is no
big deal - and one also looks out at the horizon.

Walt BJ

I hate to say it Ed but for once Tarver is right. The first *differential*
of velocity is acceleration. The first integral would be distance covered. I
understood perfectly what you meant though and envy you that experience.

Integral A dt = V0 + At =V


I've no idea what he means by this though!

John

It's basic calculus. Try this one in English units: if you drop an object the
function for determining how far it has fallen is X=16T^2, where X is the
distance travelled in feet and T is the time in seconds. The first derivative
is V = 32T where V is instantaneous velocity expressed in feet per second. The
first derivative of V, and the second of X, is A = 32 feet/second/second which
is the acceleration due to gravity. Integration is the reverse process. This
function doesn't take into account drag, but if you drop a bowling ball from
the top of a 10 story building drag is negligible.


Dan, U. S. Air Force, retired

WaltBJ wrote:

SNIP:
Ed Rasimus wrote:
Now, let's put to bed this idea of accelerating through the mach
straight up.
A couple reminders:
1) with a thrust to weight atio of 1.6:1 the Streak Eagle is
distinctly higher powered than anything any of us flew in the service.
2) It's shedding weight in full afterburner during the takeoff and
climb. I don't know what the fuel consumption of an F15 full-out is
but it's certainly over a ton a minute, so the T/W is increasing.
3) The only comparision I have experience with is the F104B on an AB
go-around at the end of a mission but with 1500 pounds of fuel reaming
a B model with 2 AIM9s weight about 16300. With 18000 pounds of thrust
it was very sprightly indeed. Thing was, that 18000 pounds of thrust
is measured in static condions. I have seen the fuel flow gauge on
both the F104s and the F4s rise from about 8500pph (per engine) on
pre-takeoff run up to 12000pph at 600 KIAS on level acceleration after
takeoff, obviously due to ram effect. Since jet thrust has a linear
relation of fuel burn - the thrust to weight ratio in flight cannot be
determined from thrust developed while sitting still on the ground.
Note that I do not know what is happening in the afterburner; the only
correlation I ever heard of was the AB fuel flow was about 4 times
that of the fuel flow to the engine itself. Also, the J79 manual
figure in AB for takeoff was 750 pounds per minute - per engine. FWIW
the engine fuel flow is determined by the necessity of keeping the
total air flow/fuel flow ratio right around 55 to 1. ( Lots more air
than stoichiometric needs to keep the engine from melting.)
4) So what I'm saying is that there is no doubt in my mind that a
lightened F15 with a minimum mission required fuel load could and did
exceed Mach 1 climbing vertically.
5) BTW with Jeff Ethell's flying experience and the highly visible
attitude direction indicator in an F15 why question his statement that
they were indeed vertical? Checking a vertical climb on the gyro is no
big deal - and one also looks out at the horizon.

Walt BJ

I can't compete with all you knowledgeable guys with the maths or actual
flying experince, but I thought I'd just contribute this..........

The Sukhoi P-42 - a modified Su-27 Flanker which took all the time-to-climb
records from the Streak Eagle - was similarly modified with tweaked engines
and lightened airframe.

It had thrust-to-weight ratio was almost 2:1 at takeoff.

The following is an extract from Andrei Fomin's book on the Su-27 :-

"The fighters engines were augmented, with the thrust of each engine
increasing by more than 1,000 kgf (in FAI reports a thrust of 2x13,600 kgf
was mentioned and the engines were presented under the designation of
R-32). The steps taken gave the P-42 a unique thrust-to-weight ratio
equalling almost 2 at takeoff. As a result, the P-42 was able to gather
speed and break through the sonic barrier when climbing".

It doesn't actually say 'climbing vertically' - but it does say supersonic
whilst climbing.

My page on the P-42 is at :- http://www.duffeyk.fsnet.co.uk/p-42.htm and
the list of some of the P-42's 27 world records is at :-
http://www.duffeyk.fsnet.co.uk/p42_records.htm

++++++++++++++++++++++++++++++++++++++++++++++++++ ++++++++++++++++
Ken Duffey - Flanker Freak & Russian Aviation Enthusiast
Flankers Website - http://www.flankers.co.uk/
++++++++++++++++++++++++++++++++++++++++++++++++++ ++++++++++++++++

What the McAir guy said was true. The profile was a published one that
kept FCF and acceptance flights out of the airport traffic pattern. They
weren't supersonic, however.

Jim Thomas

Harry Andreas wrote:


I watched F-15s do this at St Louis airport back in the 80's.
What did they call it? A "Trojan takeoff"?

The Macair guy claimed they used this profile because it kept the aircraft
noise over the airport and didn't disturb the neighbors as much.
He kept a straight face while he said it, too.
I admired him for that.

In article , B2431
writes
It's basic calculus.

I'm not too sure if 'basic' and 'calculus' sit too well together

Try this one in English units: if you drop an object the
function for determining how far it has fallen is X=16T^2, where X is the
distance travelled in feet and T is the time in seconds. The first derivative
is V = 32T where V is instantaneous velocity expressed in feet per second. The
first derivative of V, and the second of X, is A = 32 feet/second/second which
is the acceleration due to gravity. Integration is the reverse process. This
function doesn't take into account drag, but if you drop a bowling ball from
the top of a 10 story building drag is negligible.

The best bit I liked was deriving the equations of motion from the three
basic dimensions 'L', 'M' & 'T' (distance, mass, time).

--
John