[travior]

Assuming a linear rate of compromise as you turn away from zero degrees (parallel to the direction of travel) with zero degrees being 0% compromised and 180 degrees being 100% compromised: 1% compromised would be 180/100= 1.8 degrees of misalignment with direction of travel. 5% would be 9.0 degrees out.

This does not take into consideration things like dead-band, minimum excitability states, etc of the sensor.

(BTW, the older style controllers are not so tempermental. They mearly use the input from the brake pedal switch to activate the brake output at a preset level that was also manually adjustable.)

[hurley_108]

travior wrote:

Assuming a linear rate of compromise as you turn away from zero degrees (parallel to the direction of travel) with zero degrees being 0% compromised and 180 degrees being 100% compromised: 1% compromised would be 180/100= 1.8 degrees of misalignment with direction of travel. 5% would be 9.0 degrees out.

This does not take into consideration things like dead-band, minimum excitability states, etc of the sensor.

My thinking did not go so far as to quirks of the sensor, just geometry. The thing is, it's not linear. I'll give you a hint: if you mount it perpendicular to the direction of travel, it will do nothing. If you mount it completely backwards, it could actually function again, but it'll think you're in reverse.

Quote:

(BTW, the older style controllers are not so tempermental. They mearly use the input from the brake pedal switch to activate the brake output at a preset level that was also manually adjustable.)

Yes, they kept trying to sell me on one of those kind, but my car is just a Corolla, and I want to take as much stress off it as I can.

[Regina]

That’s why I like a surge brake. Backing up the trailer is a bit time consuming because you have to get out and slip the pin in but that’s only if you’re reversing for a distance.

[Blue_Nose]

The acceleration of the car can be broken up into two components - the component in the direction of the crooked sensor, and the component perpendicular to the sensor.

That leaves us with a simple right triangle, the hypotenuse being the vehicle acceleration, and the base being the sensed acceleration.

A 1% error means the sensed acceleration is 99% of the vehicle acceleration, and trignometry does the rest:

cos(angle) = 0.99
angle = 8.1 degrees

same for 5% error:

cos(angle) = 0.95
angle = 18.2 degrees.

[hurley_108]

Blue_Nose wrote:

The acceleration of the car can be broken up into two components - the component in the direction of the crooked sensor, and the component perpendicular to the sensor.

That leaves us with a simple right triangle, the hypotenuse being the vehicle acceleration, and the base being the sensed acceleration.

A 1% error means the sensed acceleration is 99% of the vehicle acceleration, and trignometry does the rest:

cos(angle) = 0.99
angle = 8.1 degrees

same for 5% error:

cos(angle) = 0.95
angle = 18.2 degrees.

Yup. That's what I figured. I drew an angle of 8 degrees, to get an idea of what it means. Visually, the brake controller looks quite a bit straighter than that.

We used to use this small angle behaviour in my classes:

For very small theta
cos(theta)=1
sin(theta)=theta
tan(theta)=theta

But until now, I never had a real world application of this, or an impression for how big "very small" can be.

[Blue_Nose]

More of a logic problem than science, but interesting:

Little Red Riding Hood is walking down a wooded path when the Big Bad Wolf jumps out and grabs her basket of food for her grandmother. Instead of just eating the food, the wolf poses this question to her:

"If you guess correctly what I will do with your basket of food, you can have it back. If you don't guess correctly, I will eat it."

What should little Red Riding Hood say to get it back?

[Pseudonym]

"You will eat it."

Caught in his own paradox, the wolf's head will explode and Red can take her gore-covered basket on her merry way.

EDIT: Alternatively, she could simply repeat what he told her he would do conditionally, but that is boring and has no exploding heads.

[Blue_Nose]

Pseudonym wrote:

"You will eat it."

Caught in his own paradox, the wolf's head will explode and Red can take her gore-covered basket on her merry way.

EDIT: Alternatively, she could simply repeat what he told her he would do conditionally, but that is boring and has no exploding heads.

If she says he will eat it and she's right, he eats it and then she can have it back - presumably she wouldn't want it at that point .

[Pseudonym]

[Blue_Nose]

My thinking was that she tell him that he won't eat it - since he said he'd eat it IF she was wrong, he's not going to eat it until she's proven wrong.

So the condition of being wrong can't be possibly verified (he's caught in a catch-22), he has to conclude she was correct, and give it back.

The only problem I can see with that logic is that the wolf might have ment that she had to predict what he planned on doing, thus the requirement that the fate of the basket be determined before the final decision doesn't apply.

[Blue_Nose]

New one that will involve some math:

In the diagram below there's a crate with some barrels of various sizes piled inside. The diameter and weight of the barrels are given, and your goal is to determine how much weight each of the little men holding up the crate need to carry.

(assume the crate itself is of negligible weight).

Attachment:

weight.PNG [ 11.96 KiB | Viewed 66 times ]

[Blue_Nose]

here's a hint to get you started:

let's say the width of the crate is 10 (it's something else that needs to be determined). The green barrel is 3 away from the left guy and 7 away from the right guy (horizontally). That means the left guy is holding 7/10 of the weight of that barrel and the right guy is holding 3/10 of the weight. In this case you can simply swap the distances to each guy, divide it by the total width, and you get the fraction of that particular weight that each guy carries.

The trick, obviously, is using the information given to find the locations of the barrels.

[hurley_108]

The guy on the left is carrying 7.41232, the guy on the right is carrying 6.58768.

Attachment:

File comment: My work on paper.

DSC_5819.JPG [ 74.21 KiB | Viewed 40 times ]

(I actually worked out A for B and B for A, but it became clear that I was doing it backwards when the guy closer to the bigger mass was carrying less, so my statement at the top of this post is my final answer.)

[Blue_Nose]

Good work!

[hurley_108]

Thanks! The centre-centre distances worked out nicely.

I recently rediscovered my TI-86, after misplacing it for almost two years in our last move. I was happy to put it to productive use again!