inverted spin recovery explanation

" An interesting fact, which is not obvious to many folks,
including
some aerobatic pilots (judging by the number of loop into the ground
accidents) is that the radius of any turn, up, down, sideways or
whatever, is a function of the square of TRUE airspeed, which is of
course a function of density altitude and calibrated airspeed.

So, if the density altitude increases your true airspeed by 5mph,
you get a 5mph^2 impact on your radius. This kind of change in radius
can ruin your day if you are playing down near the dirt.

This velocity^2 thing is also why the reverse cuban or loop down is
a real killer. If you start the pull with X knots too many, you will
use X^2 more radius for the 1/2 loop, throw in an increase in TAS of
say Y due to density altitude and you are into (X+Y)^2 more radius ...
not good. If you have not left margin either in terms of available G
or altitude you are either gonna high speed stall on the way down (and
hit the ground) or hit it on the arc.

I think this may need a little more explaining even if only for my
understanding. I am very new to aerobatics.

So if I normally commence a loop at 100 knotts but get the entry speed wrong
and start at 105 knots then my loop (assume horizontal plane and constant
speed for simplicity) will be

New_Loop_Diameter=Old_Loop_Diameter x New_Speed ^2 / Old_Speed ^2
i.e. a factor of 1.103.

A bad entry of 15 knots over speed would have a factor of 1.323.
But a target speed of 200 but entry of 215 would have a factor of 1.156.

If my understanding is not correct then please explain why. I prefer to
understand the physics/maths before I attempt some of these manoeuvres.

Anyone care to formulate what happens when speed ( or "G") are not constant?

Yes unfortunately while the radius is a function of velocity ^ 2, it
is also a function of a great many other things. The main point is to
recognize the non-linear relationship between speed and radius, and to
then recognize that density altitude changes produce non-linear
effects on radius.

I don't recommend you do anything with the math except make a big
'ahhhhhhh' sound and let it cause a sensible sense of dread in you
whenever you pull towards the ground.

By the way, a minimum radius pull is at a bit above the stall speed
so if you pull to just before the buffet you are pretty close
regardless of airspeed.

Cheers,

Peter

"Peter Ashwood-Smith C-GZRO" wrote in
message om...
" An interesting fact, which is not obvious to many folks,
including

I don't recommend you do anything with the math except make a
big
'ahhhhhhh' sound and let it cause a sensible sense of dread in you
whenever you pull towards the ground.

By the way, a minimum radius pull is at a bit above the stall
speed
so if you pull to just before the buffet you are pretty close
regardless of airspeed.

Hopefully someone isn't flying the bottom of a loop near stall
speed. Isn't the minimum radius turn going to be accomplished at
corner velocity and max-G pull?

Al

"DaBear" wrote in message
...
"Peter Ashwood-Smith C-GZRO" wrote in
message om...
" An interesting fact, which is not obvious to many folks,
including

I don't recommend you do anything with the math except make a
big
'ahhhhhhh' sound and let it cause a sensible sense of dread in you
whenever you pull towards the ground.

By the way, a minimum radius pull is at a bit above the stall
speed
so if you pull to just before the buffet you are pretty close
regardless of airspeed.

Hopefully someone isn't flying the bottom of a loop near stall
speed. Isn't the minimum radius turn going to be accomplished at
corner velocity and max-G pull?

Yes, turn rate (or time in the pull) is also a factor and max turn rate
and min turn radius are maximized if married with max available radial g
at corner. You should actually throttle up if you're behind corner!!!!
But you should never be in this situation going through a topside gate.
The airspeed should be married to the known radial g profile for your
airplane or a roll exit initiated IMMEDIATELY!!
The trick with the gate apex is not to go through at a higher airspeed
than the radial g profile you are using for the airplane will allow
through the backside commit. If the airspeed is too high through the
gate, roll should be used to exit instead of pull.
In low altitude demonstration work, the time to do your math is on the
ground. All you need to know in the air are your commit numbers. You
have them at the top or you don't...period! If you are going through a
top gate and ANY of the numbers are off and you don't execute a roll
save, you are well on your way to becoming a statistic!
I've attended more than a few funerals in the fifty years I've been
associated with low altitude acro. It's a totally unforgiving
environment!
Dudley Henriques
International Fighter Pilots Fellowship
Commercial Pilot/ CFI Retired

For personal email, please
replace the at with what goes there and
take out the Z's please!
dhenriquesZatZearthZlinkZdotZnet

Hopefully someone isn't flying the bottom of a loop near stall
speed. Isn't the minimum radius turn going to be accomplished at
corner velocity and max-G pull?

Yes, turn rate (or time in the pull) is also a factor and max turn rate
and min turn radius are maximized if married with max available radial g
at corner. You should actually throttle up if you're behind corner!!!!


Question: how does one compute or determine cornering velocity for a
specific aircraft? Must that be done through flight testing, or is there a
mathmatical relationship to the stall speed/etc?

Specifically, does anyone know the cornering V for a Decathlon 160-CS?

Thanks!

Ed wrote:
Hopefully someone isn't flying the bottom of a loop near stall
speed. Isn't the minimum radius turn going to be accomplished at
corner velocity and max-G pull?

Yes, turn rate (or time in the pull) is also a factor and max turn rate
and min turn radius are maximized if married with max available radial g
at corner. You should actually throttle up if you're behind corner!!!!

Question: how does one compute or determine cornering velocity for a
specific aircraft? Must that be done through flight testing, or is there a
mathmatical relationship to the stall speed/etc?


Do a Google search for 14cfr23.335.pdf

Specifically, does anyone know the cornering V for a Decathlon 160-CS?

With the above, you can calculate it for max gross weight.
For low speed aircraft I think it is just Va.
Look in the aircraft manual, it should have a V-n diagram.

(Peter Ashwood-Smith C-GZRO) wrote:

minimum radius pull is at a bit above the stall speed
so if you pull to just before the buffet you are pretty close
regardless of airspeed.

I think everyone agrees that you want to generate max lift
for minimum radius pullout, which by defintion implies Clmax
aka stalling AOA.

On the subject of airspeed, yes theoretically the minimum
radius will be achieved at the max G at which stalling AOA
may be maintained because the maneuver is completed in less
time, and thus there is less time for earth's gravity to pull
the aircraft down, ergo less altitude loss.

However this is potentially a very dangerous procedure if
not performed perfectly.

Many people like to wax eloquently upon what they would do
in various emergencies. They say that they would stop the
prop after an engine failure to extend their glide, or that
they would turn back after takeoff if they experienced an
engine failure.

Theoretically speaking, they would be correct. However if
they tried that fancy stuff in real life without considerable
practice they would quite likely kill themselves.

The critical, over-riding factor in a pullout is to get to
the stalling AOA. Yes, adding power can theoretically
somewhat improve things, but it will also kill you if you
aren't already at (and maintain) the stalling AOA - remember
radius is a function of velocity SQUARED - and you might over-G
and break the aircraft, or black out.

Increasing the G in a vertical pullout is a very dangerous
trick, especially in an ad-hoc, unpracticed scenario. Are the
benefits worth the potential cost?

Choose a gate altitude for your radius, with margin for error.
Choose a gate airspeed to keep your G within limits.

--
aboyd

Thanks for getting this discussion pointed toward the mathmatics, Andrew.
A Google search of "V-n diagram" pulls up some really good articles on
recovery from a vertical dive that explain in easy to understand terms.