MacCready theory in wave

Following some fun discussions with Kempton Izuno I worked out MacCready theory in wave. It turns out we should fly faster.

http://faculty.chicagobooth.edu/john...ve_macredy.pdf

Enjoy! Let me know if you see bugs.

John Cochrane

At 05:20 10 November 2016, John Cochrane wrote:
Following some fun discussions with Kempton Izuno I worked out MacCready
theory in wave. It turns out we should fly faster.

http://faculty.chicagobooth.edu/john...ve_macredy.pdf

Enjoy! Let me know if you see bugs.

John Cochrane


Faster into wind, same speed as for thermals cross-wind, slower than
inter-thermal down-wind.

torstai 10. marraskuuta 2016 7.20.04 UTC+2 John Cochrane kirjoitti:
Following some fun discussions with Kempton Izuno I worked out MacCready theory in wave. It turns out we should fly faster.

http://faculty.chicagobooth.edu/john...ve_macredy.pdf

Enjoy! Let me know if you see bugs.

John Cochrane

Good read as usual, thanks. But:

"In classic thermal lift, the thermals drift with the wind, so MacCready theory is unaffected by wind speed."

is simply not true. Windspeed inside thermal column can easily be only 50% of what it is outside thermal. Just think what would happen if wind speed would be same everywhe thermals would be completely round and symmetrical no matter what the windspeed is as there would be no shear to distort the cylindrical shape.

Actually, it turns out it's not the same crosswind. Since you have to crab in to the wind, and since wave lift does not drift you cross wind, you also fly faster in crosswind. Not as much as upwind. But in 40-60 mph crosswinds, not uncommon in wave, the effect is substantial.

John Cochrane

On Thursday, November 10, 2016 at 6:59:10 AM UTC-8, krasw wrote:
torstai 10. marraskuuta 2016 7.20.04 UTC+2 John Cochrane kirjoitti:
Following some fun discussions with Kempton Izuno I worked out MacCready theory in wave. It turns out we should fly faster.

http://faculty.chicagobooth.edu/john...e_macredy..pdf

Enjoy! Let me know if you see bugs.

John Cochrane

Good read as usual, thanks. But:

"In classic thermal lift, the thermals drift with the wind, so MacCready theory is unaffected by wind speed."

is simply not true. Windspeed inside thermal column can easily be only 50% of what it is outside thermal. Just think what would happen if wind speed would be same everywhe thermals would be completely round and symmetrical no matter what the windspeed is as there would be no shear to distort the cylindrical shape.

Hmm,

I think it's the vertical component that distorts the shape, not the horizontal wind. We agree that a parcel of air in the core is rising faster than air on the edge of the thermal. Therefor it's slope is more vertical. It take less time to climb 1000 feet than the parcel next to it. That shorter time means it is blown downwind less than slower vertical parcels and therefor the core tends to pile up on the upwind side of the thermal.

Matt

On Thursday, 10 November 2016 17:27:32 UTC+2, Matt Herron Jr. wrote:

Hmm,

I think it's the vertical component that distorts the shape, not the horizontal wind. We agree that a parcel of air in the core is rising faster than air on the edge of the thermal. Therefor it's slope is more vertical. It take less time to climb 1000 feet than the parcel next to it. That shorter time means it is blown downwind less than slower vertical parcels and therefor the core tends to pile up on the upwind side of the thermal.

Matt

I was talking about horizontal wind field. What you say makes no sense.

Enjoy! Let me know if you see bugs.

John Cochrane

Good article, John. Now, if I was proof-reading it, I'd suggest adding a few more axis labels to the plots and the legends. On P1, the sentence "Going upwind to wave lift is just like flying through no wind to thermal lift.." should be changed to "Going upwind in wave lift is just like flying through no wind in thermal lift...". My first reading of that sentence was that the pilot was pushing upwind in zero lift (or the frequent heavy sink) to get to the wave band, whereas your analysis assumes that the pilot is in wave lift constantly.

My 2c.

DH
TX

On Thursday, November 10, 2016 at 9:26:31 AM UTC-8, krasw wrote:
On Thursday, 10 November 2016 17:27:32 UTC+2, Matt Herron Jr. wrote:

Hmm,

I think it's the vertical component that distorts the shape, not the horizontal wind. We agree that a parcel of air in the core is rising faster than air on the edge of the thermal. Therefor it's slope is more vertical. It take less time to climb 1000 feet than the parcel next to it. That shorter time means it is blown downwind less than slower vertical parcels and therefor the core tends to pile up on the upwind side of the thermal.

Matt

I was talking about horizontal wind field. What you say makes no sense.

OK, lets take another shot at it. Would you agree that hypothetically if the air in the thermal was not rising then the windspeed in the "not rising thermal" would be the same as the surrounding windspeed? (I neglect the effect of rotational speed of the "thermal" which would increase windspeed on the downwind portion of rotation and reduce windspeed on the upwind portion of rotation). If so, then it is the vertical velocity component of the thermal that changes its shape.

Also, the horizontal windspeed in a thermal cannot be 50% less than the surrounding windspeed. This is a myth. If this were true, then I could extract way more energy out of a thermal by flying upwind inside of it, and downwind outside of it (like dynamic soaring) My velocity would build up and I could use that kinetic energy to climb...

On Wednesday, November 9, 2016 at 9:20:04 PM UTC-8, John Cochrane wrote:
Following some fun discussions with Kempton Izuno I worked out MacCready theory in wave. It turns out we should fly faster.

http://faculty.chicagobooth.edu/john...ve_macredy.pdf

Enjoy! Let me know if you see bugs.

John Cochrane

John,

Help me understand the goal, and assumptions. Are we trying to maximize XC speed assuming there is a long band of constant lift at the same altitude and we are traversing 90 deg to the wind? Or are we trying to maximize climb rate so we can glide to the next area of lift? Or are we trying to calculate speed to fly between 2ndary and primary upwind?

Thanks,

Matt

torstai 10. marraskuuta 2016 20.48.18 UTC+2 Matt Herron Jr. kirjoitti:
On Thursday, November 10, 2016 at 9:26:31 AM UTC-8, krasw wrote:
On Thursday, 10 November 2016 17:27:32 UTC+2, Matt Herron Jr. wrote:

Hmm,

I think it's the vertical component that distorts the shape, not the horizontal wind. We agree that a parcel of air in the core is rising faster than air on the edge of the thermal. Therefor it's slope is more vertical. It take less time to climb 1000 feet than the parcel next to it. That shorter time means it is blown downwind less than slower vertical parcels and therefor the core tends to pile up on the upwind side of the thermal.

Matt

I was talking about horizontal wind field. What you say makes no sense.

OK, lets take another shot at it. Would you agree that hypothetically if the air in the thermal was not rising then the windspeed in the "not rising thermal" would be the same as the surrounding windspeed? (I neglect the effect of rotational speed of the "thermal" which would increase windspeed on the downwind portion of rotation and reduce windspeed on the upwind portion of rotation). If so, then it is the vertical velocity component of the thermal that changes its shape.

Also, the horizontal windspeed in a thermal cannot be 50% less than the surrounding windspeed. This is a myth. If this were true, then I could extract way more energy out of a thermal by flying upwind inside of it, and downwind outside of it (like dynamic soaring) My velocity would build up and I could use that kinetic energy to climb...

I would say that if you have a thermal without vertical speed you have no thermal. Yes, vortex-like vertical structure of thermal bubble affects vertical shape of thermal, but that has nothing to do with horizontal wind discussed here. And no, it is not a myth, I and many others can see it with out own eyes using modern wind measusing inertial variometer. Usually windspeed difference between thermal center and surrounding is less that 50%, maybe 20-30%, but in well formed cloudstreet it is almost a rule that windspeed halves in best lift. There is not a shadow of doubt that thermal acts as a "semi-transparent" barrier to surrounding windfield. If the wind would not change, we would not need the skill of centering thermal, one single centering correction at the beginning would be enough since thermal would be perfectly round and symmetrical. I'm still waiting to find one that fits the description.