Streamliner Physics<zËitle> </head> <body link=blue�6link=purple> <div align="center"> <center> <table border="1"�7idth="700" bgcolor="#F7F7F7" bordercolor="#000000" cellspacing="0" cellpadding="�(N �)> <tr> �!�!td�7idth="100%" bordercolor="#FFFFFF" bgcolor="#FFFFE6"> Streamliner Physics<y:> �!�!zËd> �!�!zËr> </center> <tr> �!�!td�7idth="100%" bordercolor="#FFFFFF" bgcolor="#FFFFE6"> by Nick Demma - Updated Feb 20Ñ0ü0Ä 2006<u‹ont> </td> </tr> <center> �!�!tr> <td width="100%" bordercolor="#FFFFFF"> Purpose: The purpose of�4his analysis is to show some of the practical consequences of the physics associated�7ith riding streamliners. In other�7ords, what's it like�4o ride one of those things?<u‹ont> There are many good sources of information about bicycle�0hysics, like�4his: <a href="http:]åwww.legslarry.beerdrinkers.co.ukzËech/SpeedAndPower.htm">http:]åwww.legslarry.beerdrinkers.co.ukzËech/SpeedAndPower.htm<tæ><u‹ont> Procedure: Use�4he information from the web site (above)�4o figure out�4he equations�7hich describe the power Vs speed for�4hree different bikes. The first is the upright bike; the second is the recumbent with�4he full foam fairing; the third is�4he recumbent�7ith the full hard shell fairing. Simulate a series of hills by assembling them out of a bunch of hyperbolic tangent functions,�4hen give�4he bikes an initial speed and send�4hem coasting down the hill. Also show�7hat happens when streamliners try to ride with�5pright bikes.<u‹ont> Data: The�7eb site gives the speed at 250 2 2 2 2atts of power output and�4he�0ower at 40 Km/Hr. From these two points�7e can find an equation�4hat describes the power as a function of�4he speed. Let's�7ork through this for�4he�5pright bike. All calculations are done using the meter-kilogram-second (i.e. metric) because our system is utterly idiotic. In deference�4o those who want�4o understand�4he results, the answers are converted to familiar units. For the standard bike in�4he�5pright�0osition,�7e have�4his: At �(ry�)0 Watts,�4he�5pright bike goes �(Nã�) Km/Hr or 8.0556 mzt. To go 2 2 20 Kmfðr or 11.�1 m/s,�4he�5pright bike needs 62�(N��)Watts. For the recumbent bike�7ith the full foam fairing,�7e have�4his: At �(ry�)0 Watts,�4he bike goes 51 Km/Hr or .167 mzt. To go 2 2 20 Kmfðr or 11.�1 m/s,�4he bike needs ª5 Watts. For the recumbent bike�7ith the full hard shell fairing,�7e have�4his: At �(ry�)0 Watts,�4he bike goes 69 Km/Hr or .167 mzt. To go 2 2 20 Kmfðr or 11.�1 m/s,�4he bike needs 75 2 2 2 2atts.<u‹ont>�!�!y:> The drag force due�4o rolling resistance is proportional�4o the speed and the drag force due�4o wind resistance is�0roportional to�4he square of�4he speed. Since�4he�0ower is the force times the speed,�4he�0ower needed to overcome the rolling resistance is proportional�4o the square of the speed and the power needed�4o overcome�4he�7ind resistances is�0roportional to�4he cube of�4he speed. Let's let x = the speed squared and let's let<u‹ont>�!�!font size="2" face="Arial">y =�4he speed cubed. The�0ower as a function of speed is�4herefore:<u‹ont>�!�!y:> Power = a * x + b * y = z<u‹ont> We know�4he�0ower for�4wo different speeds, so we have two equations and two unknowns:<u‹ont> a * (8.0556)^�(N��)+ b * (8.0556)^3 = 250 a * (�.1�)^�(N��)+ b * (11.�1)^3 = 5 5�(eå�)<y:> Solving this system of equations gives�5s the coefficients a and b. 2 2 2 2e now have an equation�4hat gives us�4he power at any speed. If�9ou�7ant to see it, here it is (Indeed, it is here even if you don't want�4o see it.):<u‹ont> Upright Bike Power = 0Ô0¢0¹0È0ë0Ø0ë0Ä * speed +0.42598*speed^0Ù0ü0¿br> First Recumbent Bike Power = 2 2.3660 * speed +0.071¬*speed^3 Second Recumbent Bike Power= 0Ô0¢0¹0È0ë5649 * speed +0.02580*speed^0Ù0ü0¿br> The best bike has�4he most rolling resistance and�4his is�0robably due it its greater�7eight. The�0ower is in 2 2 2 2atts and�4he speed is in meters per second. Figure 1 shows the hill. <y:> <img border=0 src="imagesu‹igure1.gif" width="50Ø0¯0¿0ü0ë" height="�(h*�)6"> Figure ° This is�4he hill. It is rather large.<u‹ont> </center> Figure �(N��)shows the speed as a function of�4he location. The upright bike is shown in black; the foam streamliner is shown in blue;�4he best streamliner is shown in red. The best streamliner is going so fast that�4he second hill is little more than a speed bump, but �4he other streamliner barely makes it over the second hill. The�5pright bike does not make it�4o the second hill. Since the point of�4his analysis is to�0oint out�7hat riding streamliners is like,�7e should�4ake a close look at the performance (and�!�?�5se�4he�4erm loosely) of the upright bike. Notice that its speed drops�4o a lower level after each of the hills that constitute the main hill. In other�7ords, the rider of�4he�5pright bike will not experience the large hill as one hill, but rather as a series of four hills�4hat are separated by�0lateaus. The streamliners are so efficient that�4hey carry the kinetic energy from the previous hill right into�4he next hill, so�4hey experience�4he descent as one big hill.<u‹ont> <center> <img border=0 src="imagesu‹igure2.gif" width="50Ó0ë" height="�(h*�)7"> Figure �(T|�) This is a�0lot of�4he speed as a function of the location.<u‹ont> </center> Figure 2 2 shows�4he distance as a function of�4he�4ime. The upright bike goes 1.�(y>�) miles and�4he best streamliner goes 2.54 miles. It is interesting to note that�4he�0resence of�4he second hill (i.e.�4he speed bump) actually increases the distance�4hat the streamliners go. The reason�7hy�4his happens is�4he going fast wastes energy even in a streamliner. Remember�4hat brief period in American�?�!istory�7hen people cared about�4he future enough�4o impose a 55 MPH speed limit? That saved fuel. The second hill converts kinetic energy into�0otential energy causing the streamliners�4o get out of�4hat high-speed energy-wasting mode. Once they have traveled farther and slowed down a bit, the hill gives�4hem back�4he energy and they�4ravel farther than�4hey would have�7ithout�4he hill. This is not to suggest�4hat going fast down the big hill is a waste of energy. It is better�4o store the energy from the hill as kinetic energy by going fast�4han to�7aste�4he energy in air resistance and have nothing left shortly after reaching�4he bottom of�4he hill.<y:> �!�!p align="left"><center><img border=0 src="imagesu‹igure3.gif" width="541" height="�(g �)7"> Figure 0Ú0ó0¹�!�!font size="2" face="Arial">This is a�0lot of�4he location as a function of�4ime.<y:> �!�!uenter> �!�!p align="left"> Figure 4 shows the speed as a function of�4ime and, for once, it looks like�4he�5pright bike is�0erforming better�4han the streamliners. After about 5 5 5.9 minutes�4he�5pright bike is going faster than�4he best streamliner. The reason for�4his is�4hat the streamliner has gone down the first hill, over�4he second and has rolled out�4o a location�4hat is 2.54 miles from�4he start (and a mile and a half ahead of�4he�5pright) while the upright bike is still on�4he biggest descent on the main hill. �!�!center> <img border=0 src="imagesu‹igure4.gif" width="50Ø0¯0¿0ü0ë" height="�(T �)5"><u‹ont> Figure 4: This is a�0lot of�4he speed as a function of time.<u‹ont> </center>If the bike's�7eights are�4he same,�4hen they all derive the same amount of energy from�4he Earth's gravitational field�7hen they go down�4he hill. However,�0ower is energy�0er second and the streamliners go faster, so�4hey derive more power from�4he hill. They derive more�0ower from the hill because�4hey are going faster and�4his power causes�4hem to go faster, which, of course, gets�4hem even more power from�4he hill, so they go even faster. This feedback mechanism is�7hat causes streamliners to go so fast down hills, and it doesn't�4ake much of a hill. There are some bike�4rails that are built on old railroad beds where there are often very long hills that have very little slope. Sometimes the slope is so small and the area is so�7ooded that�9ou can't really see the hill. The rider of a streamliner thinks "Hmmm, why am�!�? going 2 20 MPH? Must be a hill around here somewhere". �!�!br> Figure 5 shows the power as a function of�4he speed for�4he�4hree bikes. The�0oint of this is not only�4hat the streamliners require much less�0ower�4o go any�0articular speed, of equal interest is that�4he slope of the curves is much less for the streamliners. �!�?f, by some heroic effort, you manage�4o get an�5pright bike up�4o �(ry�) MPH, you will be acutely aware of�4he futility of�4rying to get it to go any faster. This doesn't happen in a streamliner. If�9ou are�4ooling along at a leisurely �(ry�) MPH in the streamliner and you want�4o sprint�4o 0Ô0³ MPH, just�0ounce on�4he�0edals and go. It�7ill respond very nicely. It does take some time�4o get going fast because�4he kinetic energy is�0roportional to�4he square of�4he speed, but it also takes a long�4ime to slow down because of this stored energy. There is one hill on one of my rides that is short and steep followed by a flat section�4hat is about four blocks long before�!�? have to slow down for a�4urn. On�4he mountain bike, I never get going fast on the hill in the first place and shortly after hitting the flats I have�4o start pedaling again and�!�?�0edal four blocks�4o the intersection. �!�?n the streamliner,�!�? give it a few�0owerful strokes at�4he�4op of the hill and�4hen coast all the way to�4he intersection. �!�!br> Figure 5 shows�4hat the best streamliner needs about 2 2 2 2 2atts�4o go 2 2 20 MPH. Since there are about 746 Watts per horsepower, this is about .28 Hp. �!�?f you drop�4he speed�4o 0Ô0³ MPH, you need only .147�?�!p (about half as much). Once we run out of oil and industrial civilization collapses,�7e may come�4o our senses and start�5sing�6ehicles that need only one sixth of a horsepower instead of using the 0Ô0³0 Hp monstrosities�4hat are advertised on TV.<u‹ont> �!�!img border=0 src="imagesu‹igure5.gif" width="50Ø0ë0Ä" height="�(g �)6"> <center>Figure 5: This is a plot of the power as a function of�4he speed.<u‹ont> </center> For a final comparison, let's see what happens�7hen somebody in a streamliner tries to ride with somebody on an upright bike. This is not realistic because riders of streamliners get bored out of�4heir minds�7hen going that slow so�4hey quit riding with�0eople on mountain bikes. Let's suppose that each rider is going�4o put out �(eå�)0 Watts when�0edaling. The rider of�4he�5pright bike will have to�0edal all�4he�4ime to maintain any kind of reasonable speed, which will actually be 16.62 MPH. To stay�7ith the upright bike, the rider of�4he streamliner�7ill pedal when�4he speed drops�4o 1 MPH slower�4han the other bike and�4hen coast when�4he speed is 1 MPH greater. Figure 5 5 shows�4he speed as a function of time. The red�4race is for the streamliner and the black line is for the upright bike. Obviously�4he recumbent rider doesn't�0edal�6ery much. For a better view of just how much, Figure 7 shows the power as a function of�4ime. A closer look reveals that�4he rider is pedaling 16.5 % of�4he�4ime. Since both riders put out �(eå�)0 Watts when�0edaling,�4he�4otal energy used in the ride is proportional�4o the duty cycle. �!�?n other words, after a 100 mile ride, the rider of�4he�5pright bike will feel like he has ridden 100 miles�4hat the recumbent rider will feel like he has ridden 16.5 miles.<y:> �!�!p align=left><center><img border=0 src="imagesu‹igure6.gif" width="50Ø0¯0¿0ü0ë" height="�(eå�)�(N �)> Figure 6: This is a�0lot of�4he speed as a function of time.<u‹ont> <img border=0 src="images/figure7.gif"�7idth="54�(N �) height="207"> Figure 5 5 5: This is a plot of the power as a function of�4ime.<y:> �!�!uenter> If�4he recumbent rider�7ere riding alone and�0utting out 200 2 2 2 2atts all�4he�4ime (as did the upright rider), then his speed�7ould be 0Ú0Ë0Ò.8 MPH and he would finish�4he 100 mile ride in �(N��)hours and 0Õ0é0ó minutes instead of 6 hours for the upright rider. The recumbent rider would still use only 2 2 20Ç0· as much energy as�4he�5pright rider. Another aspect of�4he�0lots in Figure 5 5 5�4hat is interesting is that�4he coasting periods are .5 seconds long. I once rode with a group around Elm Creek Park Reserve and�4here�7as a guy on a trike following me. Because he was so low, he could see my feet at the lower part of the pedal stroke because my streamliner is open on�4he bottom. After the ride, he said "Man, you were hardly ever�0edaling!". Conclusions: �!�?f you really enjoy spending a lot of�4ime going down hills, then ride an�5pright bike;�4hey spend a lot of�4ime going down hills. �!�?n fact, they spend a lot of time going anywhere. If�9ou are a 5 5 55 year old�0erson on a ride like�4he�?�!abitat 500, then ride a good streamliner and stay with�4he group. This should be easy as long as there are no strong cross winds. A practical compromise between efficiency and survivability would be a streamlined�4rike. The simulation did not have any�7ind in it. When a head wind is present,�4he difference between an�5pright bike and a streamliner is even more dramatic. If�4he�7ind is coming from 2 20 degrees off the bow, streamliners have some limited sailing ability which makes them even more efficient. The best streamliner that�7as�5sed in�4his simulation is certainly not a practical bike. Some of�4hese bikes require a�4eam of four people just to get�4he rider in and the rider can't stop�7ithout�4he�4eam because the bottom is closed. The�0erformance of a practical machine will not be as good, but it will still be dramatically better than�4he�0erformance of a bike�7ithout a fairing. <y:> �!�!zËd> �!�!zËr> <zËable> <u(iv> <a href="..|øhatsup.htm">Back�4o the WISIL projects</a><y:> <uody> </html>  �<�/�d�i�v�>�<�d�i�v� �c�l�a�s�s�=�"�n�a�k�e�d�_�c�t�r�l�"�>� �<�f�o�r�m� �a�c�t�i�o�n�=�"�/�i�n�d�e�x�.�c�g�i�/�c�o�n�t�r�a�s�t�"� �m�e�t�h�o�d�=�"�g�e�t�"� �n�a�m�e�=�"�g�a�t�e�"�>� �<�p�>�<�a� �h�r�e�f�=�"�h�t�t�p�:�/�/�a�l�t�s�t�y�l�e�.�a�l�f�a�s�a�d�o�.�n�e�t�"�>�A�l�t�S�t�y�l�e�<�/�a�>� 0k0ˆ0c0fY cÛ0U0Œ0_0Ú0ü0¸� �<�a� �h�r�e�f�=�"�h�t�t�p�:�/�/�w�w�w�.�r�e�c�u�m�b�e�n�t�s�.�c�o�m�/�W�I�S�I�L�/�d�e�m�m�a�/�d�o�w�n�h�i�l�l�_�p�h�y�s�i�c�s�.�h�t�m�"�>�(�-�&�g�t�;0ª0ê0¸0Ê0ë�)�<�/�a�>� �/� �<�l�a�b�e�l�>0¢0É0ì0¹�:� �<�i�n�p�u�t� �t�y�p�e�=�"�t�e�x�t�"� �n�a�m�e�=�"�n�a�k�e�d�_�p�o�s�t�_�u�r�l�"� �v�a�l�u�e�=�"�h�t�t�p�:�/�/�w�w�w�.�r�e�c�u�m�b�e�n�t�s�.�c�o�m�/�W�I�S�I�L�/�d�e�m�m�a�/�d�o�w�n�h�i�l�l�_�p�h�y�s�i�c�s�.�h�t�m�"� �s�i�z�e�=�"�2�2�"� �/�>�<�/�l�a�b�e�l�>� �<�l�a�b�e�l�>0â0ü0É�:� �<�s�e�l�e�c�t� �n�a�m�e�=�"�n�a�k�e�d�_�p�o�s�t�_�m�o�d�e�"�>� �<�o�p�t�i�o�n� �v�a�l�u�e�=�"�d�e�f�a�u�l�t�"�>0Ç0Õ0©0ë0È�<�/�o�p�t�i�o�n�>� �<�o�p�t�i�o�n� �v�a�l�u�e�=�"�s�p�e�e�c�h�"�>—óXð0Ö0é0¦0¶�<�/�o�p�t�i�o�n�>� �<�o�p�t�i�o�n� �v�a�l�u�e�=�"�r�u�b�y�"�>0ë0ÓNØ0M�<�/�o�p�t�i�o�n�>� �<�o�p�t�i�o�n� �v�a�l�u�e�=�"�c�o�n�t�r�a�s�t�"� �s�e�l�e�c�t�e�d�=�"�s�e�l�e�c�t�e�d�"�>‘M‚rSÍŽâ�<�/�o�p�t�i�o�n�>� �<�o�p�t�i�o�n� �v�a�l�u�e�=�"�l�a�r�g�e�r�-�t�e�x�t�"�>e‡[WbáY'�<�/�o�p�t�i�o�n�>� �<�o�p�t�i�o�n� �v�a�l�u�e�=�"�m�o�b�i�l�e�"�>0â0Ð0¤0ë�<�/�o�p�t�i�o�n�>� �<�/�s�e�l�e�c�t�>� �<�i�n�p�u�t� �t�y�p�e�=�"�s�u�b�m�i�t�"� �v�a�l�u�e�=�"ˆhy:�"� �/�>� �<�/�p�>� �<�/�f�o�r�m�>� �<�/�d�i�v�>� � �