[math-fun] Archimedean dog bowl causes fire in Santa Rosa
FYI -- So much for MythBusters... I wonder what Arthur C Clarke would say about this: http://zebu.uoregon.edu/~probs/therm/sunstrok/sunstrok.html http://sanfrancisco.cbslocal.com/2013/05/02/shiny-dog-bowl-blamed-in-santa-r... Shiny Dog Bowl Blamed In Santa Rosa Fire May 2, 2013 11:59 PM SANTA ROSA (CBS SF)  A dogÂs water bowl was being blamed for starting a fire at its ownerÂs Santa Rosa home, according to fire officials. North Bay firefighters called it is one of the most unusual fire calls theyÂve ever had. Perry and Shay Weisbrich said they had to call 9-1-1 after their dog TobyÂs metal bowl reflected a concentrated beam of sunlight onto the side of their house  a beam so powerful, the wood started to burn. ÂI just looked outside a minute and saw what i thought was steam. said Shay Weisbrich. ÂA big plume of it through the glass door.. So I went over there thinking, ÂthatÂs not right, not normal. And it was smoke! The Bennett Valley Fire Department responded before the fire got out of control. As for Toby, the Weisbrichs said heÂs getting a new dish: a plastic bowl.
Once a long time ago I thought maybe I needed to call 9-1-1 about something. But I never called them -- after the 9, I was totally stumped trying to find the hyphen on my phone. --Dan On 2013-05-04, at 11:10 AM, Henry Baker wrote:
Perry and Shay Weisbrich said they had to call 9-1-1 after their dog Toby’s metal bowl reflected a concentrated beam of sunlight onto the side of their house — a beam so powerful, the wood started to burn.
not that i want to try this, but what shapes would work? bob baillie --- Henry Baker wrote:
FYI -- So much for MythBusters... I wonder what Arthur C Clarke would say about this:
http://zebu.uoregon.edu/~probs/therm/sunstrok/sunstrok.html
http://sanfrancisco.cbslocal.com/2013/05/02/shiny-dog-bowl-blamed-in-santa-r...
Shiny Dog Bowl Blamed In Santa Rosa Fire
May 2, 2013 11:59 PM
SANTA ROSA (CBS SF) – A dog’s water bowl was being blamed for starting a fire at its owner’s Santa Rosa home, according to fire officials.
North Bay firefighters called it is one of the most unusual fire calls theyÂ’ve ever had.
Perry and Shay Weisbrich said they had to call 9-1-1 after their dog Toby’s metal bowl reflected a concentrated beam of sunlight onto the side of their house — a beam so powerful, the wood started to burn.
“I just looked outside a minute and saw what i thought was steam.” said Shay Weisbrich. “A big plume of it through the glass door.. So I went over there thinking, ‘that’s not right, not normal.’ And it was smoke!”
The Bennett Valley Fire Department responded before the fire got out of control.
As for Toby, the Weisbrichs said heÂ’s getting a new dish: a plastic bowl.
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The optimum shape would be a portion of a parabola with a focus on the area you want to burn. But this wouldn't make for a very good dog dish, unless the sun were overhead, and you wanted to burn some protruding member. Would it be more plausible if the sun first hit some other reflector, then the dog dish? Or the sun goes through a half-silvered glass plate, hits the dog dish, hits the back of the glass plate, and then hits the house. Perhaps some amateur mathematician on the Santa Rosa Fire Dept. wants to check out this story more carefully... Now if the dog dish were _rotating_, then the surface of the water in the dish would form a parabola & possibly reflect the sunlight better. To make this more efficient, put molten mercury in the rotating dog dish. But then the hazmat people would show up with their hazmat suits. At 12:40 PM 5/4/2013, Robert Baillie wrote:
not that i want to try this, but what shapes would work?
bob baillie ---
Henry Baker wrote:
FYI -- So much for MythBusters... I wonder what Arthur C Clarke would say about this: http://zebu.uoregon.edu/~probs/therm/sunstrok/sunstrok.html http://sanfrancisco.cbslocal.com/2013/05/02/shiny-dog-bowl-blamed-in-santa-r... Shiny Dog Bowl Blamed In Santa Rosa Fire May 2, 2013 11:59 PM SANTA ROSA (CBS SF)  A dogÂs water bowl was being blamed for starting a fire at its ownerÂs Santa Rosa home, according to fire officials. North Bay firefighters called it is one of the most unusual fire calls theyÂve ever had. Perry and Shay Weisbrich said they had to call 9-1-1 after their dog TobyÂs metal bowl reflected a concentrated beam of sunlight onto the side of their house  a beam so powerful, the wood started to burn. ÂI just looked outside a minute and saw what i thought was steam. said Shay Weisbrich. ÂA big plume of it through the glass door.. So I went over there thinking, ÂthatÂs not right, not normal. And it was smoke! The Bennett Valley Fire Department responded before the fire got out of control. As for Toby, the Weisbrichs said heÂs getting a new dish: a plastic bowl.
A slightly more optimal [shape + position] would be for each mirror to be a portion of the prolate ellipsoid with foci at the sun and at the location to be burned that passes through the location of the mirror. The various ellipsoids involved will typically be different from each other. --Dan On 2013-05-04, at 1:35 PM, Henry Baker wrote:
The optimum shape would be a portion of a parabola with a focus on the area you want to burn.
I believe that such an ellipsoid would be indistinguishable from a paraboloid, unless the second focus (the one that isn't the sun) is many thousands of miles away. Jim Propp On Saturday, May 4, 2013, Dan Asimov <dasimov@earthlink.net> wrote:
A slightly more optimal [shape + position] would be for each mirror to be a portion of the prolate ellipsoid with foci at the sun and at the location to be burned that passes through the location of the mirror.
The various ellipsoids involved will typically be different from each other.
--Dan
On 2013-05-04, at 1:35 PM, Henry Baker wrote:
The optimum shape would be a portion of a parabola with a focus on the area you want to burn.
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A shallow segment of a sphere is a close approximation to a piece of a parabaloid. And a parabaloid doesn't focus only on the axis. If the Sun is off axis a little to one side then there will be a focal point a little off axis on the opposite side - in this case the wall of the house. Brent On 5/4/2013 1:35 PM, Henry Baker wrote:
The optimum shape would be a portion of a parabola with a focus on the area you want to burn.
But this wouldn't make for a very good dog dish, unless the sun were overhead, and you wanted to burn some protruding member.
Would it be more plausible if the sun first hit some other reflector, then the dog dish?
Or the sun goes through a half-silvered glass plate, hits the dog dish, hits the back of the glass plate, and then hits the house.
Perhaps some amateur mathematician on the Santa Rosa Fire Dept. wants to check out this story more carefully...
Now if the dog dish were _rotating_, then the surface of the water in the dish would form a parabola & possibly reflect the sunlight better.
To make this more efficient, put molten mercury in the rotating dog dish. But then the hazmat people would show up with their hazmat suits.
At 12:40 PM 5/4/2013, Robert Baillie wrote:
not that i want to try this, but what shapes would work?
bob baillie ---
Henry Baker wrote:
FYI -- So much for MythBusters... I wonder what Arthur C Clarke would say about this: http://zebu.uoregon.edu/~probs/therm/sunstrok/sunstrok.html http://sanfrancisco.cbslocal.com/2013/05/02/shiny-dog-bowl-blamed-in-santa-r... Shiny Dog Bowl Blamed In Santa Rosa Fire May 2, 2013 11:59 PM SANTA ROSA (CBS SF) A dog’s water bowl was being blamed for starting a fire at its owner’s Santa Rosa home, according to fire officials. North Bay firefighters called it is one of the most unusual fire calls they’ve ever had. Perry and Shay Weisbrich said they had to call 9-1-1 after their dog Toby’s metal bowl reflected a concentrated beam of sunlight onto the side of their house — a beam so powerful, the wood started to burn. “I just looked outside a minute and saw what i thought was steam.” said Shay Weisbrich. “A big plume of it through the glass door.. So I went over there thinking, ‘that’s not right, not normal.’ And it was smoke!” The Bennett Valley Fire Department responded before the fire got out of control. As for Toby, the Weisbrichs said he’s getting a new dish: a plastic bowl.
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What you want is an off-axis paraboloid, a segment of a paraboloid that does not intersect the axis. Then the target does not obscure the incident light. -- Gene
________________________________ From: Robert Baillie <rjbaillie@frii.com> To: math-fun <math-fun@mailman.xmission.com> Sent: Saturday, May 4, 2013 12:40 PM Subject: Re: [math-fun] Archimedean dog bowl causes fire in Santa Rosa
not that i want to try this, but what shapes would work?
bob baillie ---
Henry Baker wrote:
FYI -- So much for MythBusters... I wonder what Arthur C Clarke would say about this:
http://zebu.uoregon.edu/~probs/therm/sunstrok/sunstrok.html
http://sanfrancisco.cbslocal.com/2013/05/02/shiny-dog-bowl-blamed-in-santa-r...
Shiny Dog Bowl Blamed In Santa Rosa Fire
May 2, 2013 11:59 PM
SANTA ROSA (CBS SF) – A dog’s water bowl was being blamed for starting a fire at its owner’s Santa Rosa home, according to fire officials.
North Bay firefighters called it is one of the most unusual fire calls they’ve ever had.
Perry and Shay Weisbrich said they had to call 9-1-1 after their dog Toby’s metal bowl reflected a concentrated beam of sunlight onto the side of their house — a beam so powerful, the wood started to burn.
“I just looked outside a minute and saw what i thought was steam.” said Shay Weisbrich. “A big plume of it through the glass door.. So I went over there thinking, ‘that’s not right, not normal.’ And it was smoke!”
The Bennett Valley Fire Department responded before the fire got out of control.
As for Toby, the Weisbrichs said he’s getting a new dish: a plastic bowl.
When I was a kid in Texas I rode with my Grandfather in his '39 Ford 4door to pick up something at the store. When came back to the car it was filled with smoke. A pop bottle lying on the back seat had focused the sun onto the upholstery so that it was smouldering. Brent On 5/4/2013 11:10 AM, Henry Baker wrote:
FYI -- So much for MythBusters... I wonder what Arthur C Clarke would say about this:
http://zebu.uoregon.edu/~probs/therm/sunstrok/sunstrok.html
http://sanfrancisco.cbslocal.com/2013/05/02/shiny-dog-bowl-blamed-in-santa-r...
Shiny Dog Bowl Blamed In Santa Rosa Fire
May 2, 2013 11:59 PM
SANTA ROSA (CBS SF) – A dog’s water bowl was being blamed for starting a fire at its owner’s Santa Rosa home, according to fire officials.
North Bay firefighters called it is one of the most unusual fire calls they’ve ever had.
Perry and Shay Weisbrich said they had to call 9-1-1 after their dog Toby’s metal bowl reflected a concentrated beam of sunlight onto the side of their house — a beam so powerful, the wood started to burn.
“I just looked outside a minute and saw what i thought was steam.” said Shay Weisbrich. “A big plume of it through the glass door.. So I went over there thinking, ‘that’s not right, not normal.’ And it was smoke!”
The Bennett Valley Fire Department responded before the fire got out of control.
As for Toby, the Weisbrichs said he’s getting a new dish: a plastic bowl.
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Being BOTH a dog AND a bowl owner living sort-of near Santa Rosa, I feel eminently qualified to comment on this thread: It doesn't require a sophisticated engineered design: one afternoon a cheap silvered car sunscreen managed to raise a mysterious 3 by 1 by 1/2-inch high blister in the plastic covering an interior structural column in my sedan. As a conversation starter I would ask passengers if they thought the blister might possibly be due to some kind of scary new "killer bee" sting?? Although alas they failed to prevent the blistering, the screen WAS printed with many earnestly helpful legally-motivated safety tips, including the memorable advice: "Caution: Do not operate vehicle with sunscreen in place!" "Cave canem afferentem phialam!"
On the plane, assume the foci are at (-1,0) and (1,0): The ellipse is the locus of points whose sum of distances to the foci is a constant. The ovals of Cassini is the locus of points whose product of distances to the foci is a constant. (See < http://en.wikipedia.org/wiki/File:Line_of_Cassini.svg >.) Can you guess the evolution of the locus of points whose exponentiation of their distances to the foci is a constant, as that constant increases from 0 to, say, 2 ??? (I certainly didn't!) --Dan
participants (7)
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Dan Asimov -
Eugene Salamin -
Henry Baker -
James Propp -
Marc LeBrun -
meekerdb -
Robert Baillie