Center of Gravity - Revision history

SpookySimon: /* Measure the CG / subscipting the b wo it doesnt look like wb

2024-04-26T16:30:59Z

Measure the CG: subscipting the b wo it doesnt look like w*b

SpookySimon: /* Measure the CG */ cleaning up

2024-04-26T16:29:44Z

Measure the CG: cleaning up

SpookySimon: /* Total Vehicle CG */ cleaning this bad boy up

2024-04-26T16:28:46Z

Total Vehicle CG: cleaning this bad boy up

SpookySimon: /* Total Vehicle CG */ note on image not loading

2023-01-09T19:35:59Z

Total Vehicle CG: note on image not loading

SpookySimon: minor style and links

2023-01-09T19:35:18Z

minor style and links

Benjmyn at 20:27, 25 May 2020

2020-05-25T20:27:51Z

Toaster at 17:24, 17 May 2020

2020-05-17T17:24:30Z

Toaster: Toaster moved page Center of Gravity (CG) to Center of Gravity

2020-05-17T17:23:09Z

Toaster moved page Center of Gravity (CG) to Center of Gravity

Bertaveira at 19:07, 16 May 2020

2020-05-16T19:07:52Z

Bertaveira: Starting point (still incomplete)

2020-05-16T19:05:50Z

Starting point (still incomplete)

New page

The '''center of gravity''' (also referred to as '''center of mass''' or '''CG''') isthe average location of the weight of the car. The point in space that sums the vehicles mass in a single point. To put it in simple to visualize terms, if we could suspend the car from that point only we would not witness any forces twisting the car into a specific orientation since the mass would be equally distributed in all three dimensions.
==Measure the CG==
===Total Vehicle CG===
Measuring the total planar center of gravity is fairly easy with only 4 weight scales, one under each tyre. We say total because we are not making a distinction between non-suspended and suspended mass. Make sure you're in a leveled floor so that the weight on the scales doesn't get influenced by inclination.

We can start by determining the distance of the CG to the front axle. This is also normally referred to as the distance "'''a'''". <math>a = \frac{ W_{rear} }{ W_{total} } Wb</math>

Where <math>Wb</math> corresponds to the wheelbase of the car (distance between axles), <math>W_{rear}</math> the rear weight (sum of both rear tyre scales) and <math>W_{front}</math>the front weight (sum of both front tyre scales). From this we can get the distance normally referred as '''"b"'''(from rear axle to CG) just by subtracting from the wheelbase:

<math>b = \frac{ W_{front} }{ W_{total} } Wb = Wb - a</math>

You can also apply the same formulas to find lateral location of the center of gravity. For a balanced and best performing car all around it should be in the center longitudinal line of the car but it should be measured to find if this is true for a specific car. We can call this measurement of distance of CG to the side as "'''c'''" for example and calculate it as such:

<math>c = \frac{ W_{left} }{ W_{total} } Track</math>

Once again the advised it for "'''c'''" to be half the track of the car. For cars with different front and rear tracks you can still calculate this "'''c'''".

Now for determining the '''height of the center of gravity''' we need to tilt the car around one of the horizontal axis. This could be with a tilt table or just by raising both the front or the rear wheels (as illustrated on Figure 1).[[File:Image010.jpg|link=http://www.thecartech.com/subjects/auto_eng/Center_of_Gravity.htm|right|middle|thumb|Figure 1 - Measuring height of the CG]]

[under construction - Formula missing]
==Optimum Center of Gravity==

@@ Line 7: / Line 7: @@
 We can start by determining the distance of the CG to the front axle. This is also normally referred to as the distance "'''a'''".
-<math>a = \frac{ W_{rear} }{ W_{total} } Wb</math>
+<math>a = \frac{ W_{rear} }{ W_{total} } W_b</math>
 Where <math>Wb</math> corresponds to the wheelbase of the car (distance between axles), <math>W_{rear}</math> the rear weight (sum of both rear tyre scales) and <math>W_{front}</math><span><span></span>the front weight (sum of both front tyre scales)<span></span></span>. From this we can get the distance normally referred as "'''b'''"(from rear axle to CG) just by subtracting from the wheelbase:
-<math>b = \frac{ W_{front} }{ W_{total} } Wb = Wb - a</math>
+<math>b = \frac{ W_{front} }{ W_{total} } W_b = W_b - a</math>

← Older revision		Revision as of 16:29, 26 April 2024
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−	~~<span>~~We can start by determining the distance of the CG to the front axle. This is also normally referred to as the distance "'''a'''".~~</span><br /><math>a = \frac{ W_{rear} }{ W_{total} } Wb</math>~~	+	We can start by determining the distance of the CG to the front axle. This is also normally referred to as the distance "'''a'''".

−	Where <math>Wb</math> corresponds to the wheelbase of the car (distance between axles), <math>W_{rear}</math> the rear weight (sum of both rear tyre scales) and <math>W_{front}</math><span><span></span>the front weight (sum of both front tyre scales)<span></span></span>. From this we can get the distance normally referred as '''"b"'''(from rear axle to CG) just by subtracting from the wheelbase:	+	<math>a = \frac{ W_{rear} }{ W_{total} } Wb</math>
		+
		+	Where <math>Wb</math> corresponds to the wheelbase of the car (distance between axles), <math>W_{rear}</math> the rear weight (sum of both rear tyre scales) and <math>W_{front}</math><span><span></span>the front weight (sum of both front tyre scales)<span></span></span>. From this we can get the distance normally referred as "'''b'''"(from rear axle to CG) just by subtracting from the wheelbase:

← Older revision		Revision as of 16:28, 26 April 2024
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	<span>We can start by determining the distance of the CG to the front axle. This is also normally referred to as the distance "'''a'''".</span><br /><math>a = \frac{ W_{rear} }{ W_{total} } Wb</math>		<span>We can start by determining the distance of the CG to the front axle. This is also normally referred to as the distance "'''a'''".</span><br /><math>a = \frac{ W_{rear} }{ W_{total} } Wb</math>
−
−
−	<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a={\frac {W_{rear}}{W_{total}}}Wb}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> <mi>e</mi> <mi>a</mi> <mi>r</mi> </mrow> </msub> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mi>o</mi> <mi>t</mi> <mi>a</mi> <mi>l</mi> </mrow> </msub> </mfrac> </mrow> <mi>W</mi> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a={\frac {W_{rear}}{W_{total}}}Wb}</annotation> </semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c4092ad0e7c49b01dc6f72342d413905b0238702" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.338ex; width:14.368ex; height:5.676ex;" alt="{\displaystyle a={\frac {W_{rear}}{W_{total}}}Wb}"></span>
−	~~<!-- image not loading-->~~

	Where <math>Wb</math> corresponds to the wheelbase of the car (distance between axles), <math>W_{rear}</math> the rear weight (sum of both rear tyre scales) and <math>W_{front}</math><span><span></span>the front weight (sum of both front tyre scales)<span></span></span>. From this we can get the distance normally referred as '''"b"'''(from rear axle to CG) just by subtracting from the wheelbase:		Where <math>Wb</math> corresponds to the wheelbase of the car (distance between axles), <math>W_{rear}</math> the rear weight (sum of both rear tyre scales) and <math>W_{front}</math><span><span></span>the front weight (sum of both front tyre scales)<span></span></span>. From this we can get the distance normally referred as '''"b"'''(from rear axle to CG) just by subtracting from the wheelbase:

← Older revision		Revision as of 19:35, 9 January 2023
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	<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a={\frac {W_{rear}}{W_{total}}}Wb}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> <mi>e</mi> <mi>a</mi> <mi>r</mi> </mrow> </msub> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mi>o</mi> <mi>t</mi> <mi>a</mi> <mi>l</mi> </mrow> </msub> </mfrac> </mrow> <mi>W</mi> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a={\frac {W_{rear}}{W_{total}}}Wb}</annotation> </semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c4092ad0e7c49b01dc6f72342d413905b0238702" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.338ex; width:14.368ex; height:5.676ex;" alt="{\displaystyle a={\frac {W_{rear}}{W_{total}}}Wb}"></span>		<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a={\frac {W_{rear}}{W_{total}}}Wb}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> <mi>e</mi> <mi>a</mi> <mi>r</mi> </mrow> </msub> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mi>o</mi> <mi>t</mi> <mi>a</mi> <mi>l</mi> </mrow> </msub> </mfrac> </mrow> <mi>W</mi> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a={\frac {W_{rear}}{W_{total}}}Wb}</annotation> </semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c4092ad0e7c49b01dc6f72342d413905b0238702" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.338ex; width:14.368ex; height:5.676ex;" alt="{\displaystyle a={\frac {W_{rear}}{W_{total}}}Wb}"></span>
		+	<!-- image not loading-->

	Where <math>Wb</math> corresponds to the wheelbase of the car (distance between axles), <math>W_{rear}</math> the rear weight (sum of both rear tyre scales) and <math>W_{front}</math><span><span></span>the front weight (sum of both front tyre scales)<span></span></span>. From this we can get the distance normally referred as '''"b"'''(from rear axle to CG) just by subtracting from the wheelbase:		Where <math>Wb</math> corresponds to the wheelbase of the car (distance between axles), <math>W_{rear}</math> the rear weight (sum of both rear tyre scales) and <math>W_{front}</math><span><span></span>the front weight (sum of both front tyre scales)<span></span></span>. From this we can get the distance normally referred as '''"b"'''(from rear axle to CG) just by subtracting from the wheelbase:

@@ Line 1: / Line 1: @@
-The '''center of gravity''' (also referred to as '''center of mass''' or '''CG''') is <span>the average location of the weight of the car. The point in space that sums the vehicles mass in a single point. To put it in simple to visualize terms, if we could suspend the car from that point only we would not witness any forces twisting the car into a specific orientation since the mass would be equally distributed in all three dimensions.</span>
+The '''center of gravity''' (also referred to as '''center of mass''' or '''CG''') is <span>the average location of the weight of the car. The point in space that sums the vehicles [[Mass|mass]] in a single point. To put it in simple to visualize terms, if we could suspend the car from that point only we would not witness any forces twisting the car into a specific orientation since the mass would be equally distributed in all three dimensions.</span> <!-- i think this may not be as "easy to visualize" if you do not understand the concept already-->
-==<span>Measure the CG</span>==
+==Measure the CG==
-===<span>Total Vehicle CG</span>===
+===Total Vehicle CG===
-<span>Measuring the total planar center of gravity</span><span> is fairly easy with only 4 weight scales, one under each tyre. We say total because we are not making a distinction between non-suspended and suspended mass. Make sure you're in a leveled floor so that the weight on the scales doesn't get influenced by inclination.</span>
+<span>Measuring the total planar center of gravity</span><span> is fairly easy with only 4 weight scales, one under each [[Tires|tyre]]. We say total because we are not making a distinction between non-suspended and suspended mass. Make sure floor is level so that the weight on the scales doesn't get influenced by inclination.</span>
@@ Line 31: / Line 31: @@
 ==Optimum Center of Gravity==
 ==Mass Centroid Axis==
 The Mass Centroid axis is measured in sections of the car, it's the axis, which isn't necessarily linear, which goes through every 2-d center-of-gravity. It doesn't have to be measured at every point in the car, you can approximate and get a better sense of the roll center moments, which aren't just measured on a parallel c.o.g. axis to the ground.
+[[Category:Vehicle Dynamics]]

@@ Line 7: / Line 7: @@
 <span>We can start by determining the distance of the CG to the front axle. This is also normally referred to as the distance "'''a'''".</span><br /><math>a = \frac{ W_{rear} }{ W_{total} } Wb</math>
 Where <math>Wb</math> corresponds to the wheelbase of the car (distance between axles), <math>W_{rear}</math> the rear weight (sum of both rear tyre scales) and <math>W_{front}</math><span><span></span>the front weight (sum of both front tyre scales)<span></span></span>. From this we can get the distance normally referred as '''"b"'''(from rear axle to CG) just by subtracting from the wheelbase:
@@ Line 27: / Line 29: @@
 [under construction - Formula missing]
 ==Optimum Center of Gravity==
 [[Category:Vehicle Dynamics]]

← Older revision	Revision as of 17:23, 17 May 2020
(No difference)