A tyre blow -out on a car avan can be disastrous, even fatal in severe situations. A non- pneumatic wheel (NPT) has the obvious advantage of being resistant to the DREADED FLAT TYRE . Thus, there is promise of safety. A number of tyre manufacturers have been busy developing a tyre or complete wheel to capitalize on this benefit. The best - know n NPT is dubbed the T WEEL®. The nomenclature of Michelin’s NPT is a joining of parts of the two wo rds, Tire and Wheel . The TWEEL® has application to skid -steer loaders and commercial lawn mo wers. Michelin encountered problems in the development of the TWEEL® for high speed use . One of these problems encountered by Michelin in the development of the Tweel may be a god -send for caravan wheels as they develop the ir new NPT for highway use. The design of the so-called UPTIS® is not just an improved version of the TWEEL® but a completely different operating philosophy . This paper considers the evolution of the NPT and considers how it might be beneficial in the caravan context . To illustrate, a fishtailing tale to tell gets told. Keywords : Caravan, fishtailing, snaking, UPTIS, TWEEL, NPT “ non-pneumatic ”, airless . INTRODUCTION The aspiration to improve on air inflated tyres goes back a long, long way. Carl Purdy writes in his patent filed in 1904 (Purdy, 1905) as below. Figure 1 refers. Figure 1 – Purdy’s Sp iral Spring Airless Tyre Patent “This invention relates to tires, and more particularly to the class of cushion -tires, and has for its object to provide a tire which will be extremely resilient and in which the disadvantages common to pneumatic tires will be eliminated.” Many inventions have been lodged since then and so far, only the TWEEL® has had marketing success. We must wait until 2024 before the first high speed airless tire rolls out of a Gen eral Motors (GM) production line for a highway speed use. “…probably not sooner than that .” according to Steve Cron, senior principal product engineer at 2 Michelin . He added that they have a very high lateral stiffness. (Cole, 2019) . It is the latter comment by Steve Cron that has implication for caravan fishtailing. As an overview on tyre performance generally , the National Highway and Traffic Safety Authority (NHTSA) indicate failure of a tire/wheel was the most frequ ent critical reason for a vehicle crash. (NHTSA, 2008) . Ramesh, (2020) quotes statistics of 738 deaths from 78,000 automobile crashes each year in the USA. In a press release Michelin, (2020 ) report on their “Scrapyard Survey” taken over a period spanning 2 years viz. 2013 -2015, as follows: • 12% of tyres fail due to blow -outs. • 8% fail due to irregular tyre pressure. • Amounting to 200 million such tyres each year. • In total an extrapolated 1 Billion tyres are scrapped each year world -wide. It is not surprising therefore, that there is an urgent move to migrate towards tyres that do not require inflation. These statistics also show the potential to reduce raw materials use and waste. Michelin’s UPTIS® and TWEEL® both non -pneumatic tyres, seed into a mission to conserve. The TWEEL® found success among low speed vehicles and more recently in NASA’s latest lunar rover vehicles. Currently, n on-pneumatic tyres are authorized for highway use only as a spare wh eel according to rules by NHTSA , (1990) . The UPTIS® is the hope for the next generation airless tyre to suit high speed vehicles. The UPTIS® in Figure 2 might look to be fait accompli on th e press -release photographs, b ut unfortunately , the finished product , the result of a partnership between GM and Michelin might be different, only promising to show fruit in the year 2024. The challenges are significant. The aim of this paper is to under stand some of these challenges in the context of safer caravanning . TWEEL ON SHOWROOM FLOOR UPTIS AS A FRONT WHEEL BRIDGESTONE HALVES Figure 2 - Comparison – TWEEL®, UPTIS® & Bridgestone Airless Tyres Little is known regarding the Bridgestone NPT 3 THE NON -PNEUMATIC TYRE The non-pneumatic tyre (NPT) comprises a rigid hub that gets bolted to the vehicle ax le stub, just like any other wheel . Radiating from the hub are elastomeric spokes that collapse to fa cilitate a ground engaging patch. Surrounding th e spokes, one finds a ring serving as a so -called shear beam. Since the spokes offer little support for the hub in compressive mode, the upper spokes do the work in tension. The weight carried by the hub e ffectively hangs from the circular shear beam. Steve Cron (Michelin engineer) recalls explaining (Meyer, 2018) : "The ground is not pushing directly to the bo ttom of your wheel. In the automobile, you should think of the tire as hanging. ” Figure 3 refers showing the weig ht carried by three springs and the corresponding ground reaction. Figure 3 – Hanging weight principle of tyres We test the hanging principle in Figure 3 on a random pneumatic tyre by measuring the upper tyre radii for various inflation pressures. Obviously, such an exercise is not feasible on an NPT as there is no inflation pressure to vary. Figure 4 – Pneumatic tyre hanging dimensions With the exception of the 20-psi meas urement (likely the result of rounding convention) there was no axle droop from the top of the tyre. 4 STRUCTURAL vs GEOMETRIC STIFFNESS A pneumatic tyre from the manufacturer comes with some structural stiffness that enables convenient handling, fitment a nd storage. This stiffness is obviously not sufficient for motoring hence the need for inflation. The geometric stiffening process can be visualized by inflating a bicycle inner tube. Before inflation it may lie completely flaccid on the table. However , even a small inflation pressure will bring it to life as a circular (almost) object as shown i n Figure 5. Figure 5 – Bicycle inner tube demonstrating geometric stiffness. Geometric stiffness in a pne umatic tyre is similarly achieved by the inflation pressure while the non -pneumatic shear beam must develop stiffness by virtue of structural shear and bending resistance . Geometric stiffness also applies to natural frequencies of vibration as shown by (Jia et al., 2005) . We visualiz e the increase in mode shape stiffness for a P195/60R14 tyre from their data in Figure 6: Figure 6 – Increase in vibration stiffness due to inflation pressure. 5 LATERAL STIFFNESS Lateral stiffness can be defined as the force required to deflect the tyre sideways. Brell & Thambiratnam, (2020 ) compared two identical outside dia meter tyres; one of low lateral stiffness and the other high lateral stiffness. The high lateral stiffness tyre showed a significant improvement in fishtailing energy thus lessen ing the severity of such an event . Lateral stiffness in a caravan tyre is a very desirable thing. The shear beam or tread band on a tyre must have significant structure to support the hanging axle load. Unfortunately, the NPT shear beam , as we cu rrently know it , can perform (i.e. hold the axle up) only if it has structural stiffness. Thus, it must have adequate section modulus to resist collapse yet not too stiff to allow an adequate contact patch to form with the ground . A large section modulus is associated with high lateral stiffness, the sought -after featur e for caravans. To perform some testing, Michelin equipped an Audi A4 with five times the lateral stiffness as normal. The result was reported by Michelin as “responsive handling”. (Mihalascu, 2010) Towing a cara van with tyres h aving a high lateral flexibility (i.e. low lateral stiffness) should be thought of as towing a drawbar -equipped shopping trolley – an invitation to sway wildly at every lane change. By way of contrast, laterally stiff tyres on a tandem axle or tri -axle co uld encourage dangerous oversteer in the towing vehicle, especially on, say, a downhill curve where drawbar steer might control flexible car rear tyres . While high lateral stiffness on a tri -axle may exacerbate tyre wear slightly, there ap pear no such downsides on single axle towing. Against the significant benefit of never having a flat tyre , must be weighed the amount of TWEEL® noise and just how bad the TWEEL® vibration might b e. There appear no noise and vibration test reports in th e literature. Manga, (2008) recommended in his further research section , the following: • Apply strain gages to TWEEL® spoke and run on a chassis dyno in an anechoic chamber. • Use slip -rings to get signals out. • Record acoustic signal in vicinity of TWEEL® at a range of speeds . It appears the foreshadowed research has not materialized . 6 NOISE, HEAT & VIBRATION Steve Cron ha d already tested the TWEEL® on public roads . "I had it on my car," he said. "I drove every day for four years" according to the interview by Craig Cole. (Cole, 2019) . Cron reported no issues at the time but it is generally known that the TWEEL® does have issues at the higher speeds. (Raiciu, 2009) . Cron conceded at the 2010 Simulia Customer Conf erence: “One of the challenges in TWEEL® tire development has been the noise and vibration caused by the TWEEL® tire, rolling at speeds typical of an automobile. ” (Cron, 2010) . Manga (2008) postulated the noise and vibration emanated from spoke flapping as a result of spoke buckling then retensioning. Using Finite Element Analyses (FEA) , spoke vibration was demonstrated at identical frequencies both at 60 and 80 km/h leading to a conclusion that the spokes will vibrate at th eir resonant f requency independent of rolling speed. One might ask whether the noise and vibration matter in the caravan context given the remoteness of occupants. In what appears a securing of patent protection, a modification was claimed in a patent by Delfino et al. (2017) . The reduced late ral stiffness is accomplished by reducing the overall width of the shear panel of the spoke as well as a slit that separates the spoke panel into two or more (as claimed). Here lateral stiffness is seen as a problem to be solved. The sketch in Figure 7 refers. Figure 7 – Web shear strength reduction. One of the problems preventing the TWEEL® from becoming a high -speed tyre was vibration. Vibration is influenced by the two parameters: mass and stiffness. Clearly, the T WEEL® needs a stronger and heavier shear beam to support the hanging axle than is needed for the UPTIS®. There are many mode shapes in the vibration responses in any tyre. A full comparison of vibration on these two tyres is beyond scope for this paper. However, one mode shape stands out and could well be in frequency range of resonance. This is visualiz ed in Figure 8 where the size of oscillating mass is a relevant feature. 7 Figure 8 – Vibration mode shape comparison – in analogy The lesser mass in the UPTIS® shear beam emphasizes one of the advantages of bottom support as against hanging support found in the TWEEL®. …all of which helps to appreciate the finesse of the UPTIS® design in the details to follow. CLEVER UPTIS® Whilst it was intended for automobiles (Rhyne et al 2001) , there appears an abandoning of the TWEEL® of ever becom ing a high -speed airless tyre . The UPTIS® appears not to be just an upgrade on the TWEEL®. Rather, i t represents a complete departure from the hanging principle shown in Figure 3. Performance of the UPTIS® is dependent both on the material properties and the geometry of the structure. Little is published regarding UPTIS® other than marketing hyperbole in press releas es. These are mostly of little value in an engineering sense . The rendering of physical embodiments in patent applications is an area of great interest in understanding the product under development , especially when speculating on an extension to their immediate intent and usefulness . Fortunately, Michelin patents give some insight , since disclosure of details is a precondition of the granting of a patent . Study of progre ssion of their patents also give insight. One such Michelin patent, (Miles et al., 2019) shows a row of s pring steel spokes encased in an elastomer -like poly meric . The encapsulated spoke flexes in response to the formation of a contact patch. As the wheel rotates the spokes make contact with adjoining non-flexing portions of the spokes (mounting bases) so changing the lengths of spoke s in flexure. Figure 9 shows a tracking of a single spoke through -out the flattening of the contact patch . The progress is as follows: • The spoke is approximately the shape as shown on the End View of Figure 9 • and may possibly be unflexed, pre -stressed or pre -tensioned at the point of entry into the contact patch affected zone. • At this point, the starting point of this description, R 0 is considered the natural spring rate of the spoke. • R1 is the spoke’s spring rate when the top en d of the spoke is held in place by the top mounting base and the spoke length is shortened by the support of the adjoining spoke mounting base. 8 • The spoke progresses to where it is again shortened by cont act with both top and bottom adjoining mounting bases. Here the spring rate is R 2 representing the shortened spring length in flexure . • The spoke under consideration is now leaving the contact patch affected zone still having support at the top adjo ining m ounting base reducing the spring rate to R 3. • Beyond the affected zone the spoke now reverts back to R 0. • The spring rates are not only affected by the spoke’s stiffness, as varied posit ionally, but also by the flexure of the adjoining mounting bases. • Figure 9 – Flexing of spokes showing changing spring rates In the description above it can be seen that the application and release of forces to support the wheel hub , although rapid, is a gentle and progressive process. Since late ral tyre stiffness is the mainstay of this paper to minimise fishtailing of caravans, it is competent to discuss the mechanics of stiffness to be delivered by the UPTIS®, if only to demonstrate the adaptability of the UPTIS design. It is tempting to ascri be such stiffness to St Venant’s torsion of the cross -sectio n since superficially it appears like the spoke is in simple shear. This is shown in Figure 10 where a force (F) causes a shear displacement (D). There are 13 spring st eel elements in the spoke of Figure 10 according to their patent. Although the element is encastered in a flexible matrix of an elastomer , each element plays a part in the overall lateral stiffness of the spoke. Although the flex ible matrix plays a part in the overall lateral stiffness, we study the spring steel elements in isolation (as if the elastomer were not present ). 9 Figure 10 – Shear displacement of spoke – Isometric & Elevation Views It will be noticed that in Figure 10 an angle is subtended designated  Since each strip is fixed top and bottom, this angle becomes zero and causes twist. Classical St Venant torsion can be used here using momen t of resistance in lieu of polar moment of inertia. Moment of torsional resistance can be calculated (approximatel y) from Equation 1: 𝑴𝑻=0.3 𝑥 𝑤 𝑥 𝑡3 Equation 1 To understand the behaviour of the spring steel element better, a strip of 200 gsm paper was arranged on two pieces of string, vertically separated. This is shown in Figure 11. Figure 11 – Lateral stiffness of strip element. The end fixity of the strip in (if it were in an UPTIS®) requires the angle  to be zero , thus develop the moment MB . This, in turn creates bending of double curv ature visualized as a beam in Figure 12: Figure 12 – Bending stiffness of strip element. 10 Transposing Bending Equation 1(f) from Table 8.1 Roark’s Formulas for Stress and Strains (Young & Budynas, 2002) yield a relationship for the bending moment in Equation 2. Both moments ( MT and MB , Equation 1 &Equation 2) are a product of strip width (w) and strip thickness (t). An increase in either will increase lateral stiffness. Only a small mathematical manipula tion is needed , (remain ing for future work ), to arrive at the classical rendition of stiffness ( F/D = N/mm). Sufficient for this paper’s aims to conclude that b oth St V enant’s torsion and bending across the strong axis of strip are implicated in lateral s tiffness of the UPTIS®. To produce a stiffer UPTIS® all that is needed is a smaller number of strips but wider to acquit the same vertical stiffness needs. To conclude on the UPTIS® here, there is hope for a future lateral very stiff NPT becoming availab le in the market place. To summarize on the importance of tire performance we quote Kurtz & Anderson, (1977) : “In the hierarchy of forces acting upon cars towing trailers, it is g enerally agreed that the tire forces exerted on the vehicle by the road are of primary importance. Anyone embarking on a study of the handling character istics of such vehicles would thus be wise to pay considerable attention to tire forces.” Next we re flect on the words of Fratila & Darling, (1996) seemingly expr essing surprise that the modelling did not agree with testing: “Differences in results were attributed to fact ors not included in the computer simulation such as tyre lateral stiffness…” Finally, we lament the absolute dearth of lateral stiffness values tested and published by tyre manufacturers. 11 A FISHTAILING TALE TO TELL Forensic examination of a real-life event has permitted extraction of useful oscillation details. Whilst t here are many videos posted on the Internet showing caravans towed to destruction , one Internet posting is of a caravan rig that was successfully stopped without damage . (Note the ta il lights in Figure 13). This posting was of particular value since shadow cast on the roadway were sharply defined permitting some graphical solutions to be derived. A dashcam video of the event was posted on YouTube and can be viewed her e: https://www.youtube.com/watch?v=qo -qpy0krkE Figure 13 – Stills from dashcam video (Sequence L to R) In the dashcam video, t he 4WD towing the caravan wa s overtaking a truck on a dual carriageway down a slight downward incline , getting into difficulty, according to Harvey Day, (2017 ). The speed limit for caravans on that road was 60 mph. It is hard to imagine that a truck driver would be much under 60 mph on a clear downhill run. Thus, the 4WD must have been exceeding the speed limit to be overtaking . Figure 14 – Vehicles involved in fishtailing event on the A30 into Cornwall UK. Some specifications for the vehicles in Figure 14 can be found in Table 1. Table 1 - Specifications of Vehicles Vehicle Argosy Shogun Drawbar ( Scaled ) WB=3.88m - Overall Length Long =6.347m 4900 mm Width Wide =2.286m 1875 mm Wheelbase - 2780 mm Weight M=1448 kg 2375 kg Two Tyres 185 x R14 12 Whether the Shogun driver made his l ane change too rapidly (the truck driver reported a clipping of his wing mirror ), or the interaction of the caravan with the truck bow wave started the oscillation , are not known. It is also possible that the Shogun exceeded critical velocity above which instability can occur. Critical velocity can be determined according to (Genta & Genta, 2017) : Equation 3 Where cornering Stiffness © is extrapolated from data published for a 185 x R14 tyre by Cabrera et al ., (2005) and posted to Figure 15. Figure 15 – Cornering s tiffness e xtrapolated from data by Cabrera et al., (2005) . Thus co rnering stiffness is calculated for a single axis caravan as 5333 N/deg for the total of two of these tyres . Some assumptions are needed: • A straight -line hitchpoint path is assumed. • Start of sequence is from a nominal point after the Shogun first appears. • Finish of sequence is at jack -knife . • Length of sequence considered is 9 seconds . • Road width is 7.0 m • Weight is evenly distributed and centred on intersection of axle and drawbar. • Centroidal mass moment of inertia of caravan is calculated as evenly distributed. • Hitchpoint mass moment of inertia is calculated by the parallel axis theorem. The peak angles of articulation are determined by rotating shadows into the true vertical plane to the procedure shown in Figure 16: 13 Figure 16 – Rotating shadow to extract true articulation angle The peak articulations g raphed together with those estimated, are plotted against the sequence time from the video to Figure 17: Figure 17 – Transient articulation angles. The start and finish data points were estimated while the radii at the data peaks are added by the spreadsheet software. The dotted trend line corresponds with the general direction of hitchpoint travel. This line better represents the zero -articulation point in the oscillation. To reflect this Figure 17 is redrawn, the dotted line as the abscissa. Figure 18 refers. Here it can be noted that even though towards the end the estimated caravan speed is clearly below the critical speed, the sway angle of the caravan increases. 14 Figure 18 – Adjusted articulation angles showing speed d ecay & yaw energy exchange. At each oscillation there is a phase where rotational kinetic energy is built up, to be acquitted subsequently by a disch arge phase. When so -called yaw energy exceeds the level of damping a wider sway occurs. This can be observed in Figure 18 where the sway angles increase to above 10O. It would be instructive to compare the yaw energies involved in the oscillation cycles in the radial tyres as fitted, to the TWEEL®. Unfortunately , a complexity manifests. Yaw energy is not even through -out its accumulation stroke . Here, we must agree with Pacejka & Sharp (1991) where accuracy must sometimes yield to demands of complexity. Thus, ya w energy is calculated based on average yaw velocity. We invoke Walt Disney’s ‘plausible -impossible ’ (Beaudine & Jackson, 1956) and freeze -frame a t 1.5.seconds into the fishtailing sequence to change tyres and complete the remainder of the journey on tyres that have no sideslip. Perhaps the TWEELS as fitted to the BMW (having 5X lateral stiffness) as reported in (Mihalascu, 2010) were as stiff. We will assume so. An accumula tion phase could then be replaced with a tractrix to represent the BMW Tweel®. This is shown in Figure 19: Figure 19 – Accumulation phase replaced with notional BMW Tweel® The old tyres achieved a yaw d isplacement of 9.4O in 0.5 s giving a yaw rate of 18.8 deg/s. The notional BMW Tweel® takes 2.5 s to wash off the same articulation angle of 15 9.4O giving a mere 3. 8O /s yaw rate. There are clear implications for the yaw energy to be acquitted in the disch arge phase, as follows in Table 2: Table 2 – Radial vs TWEEL® Item Radial TWEEL® Angular Velocity (Average) Critical Velocity (Equation 3) Kinetic Rotational (Yaw ) Energy Driving at speeds above the critical velocity does not mean that fishtailing necessarily occurs. It simply refers to an instability zone. A caravan rig needs initiating factors for fishtailing to manifest. There appear to be a number of these factors present in this fishtailing tale such as lane changing, truck bow wave, speed and overtaking. Then again, it might be that the tyres were just inadequate for the task. The huge difference in the calculated yaw energies support this idea. DISCUSSION The promise of never ha ving a flat tyre holds appeal . So too, never having to check tyre pressure. Fo r a caravan, these are very good things, especially given the many days a caravan typically spends at home idle. The prototype Chevrolet Bolt EV is to offer the UPTIS® sometim e in 2024 or beyond . According to the specification sheet, this car tares at 3,563 lbs, or about 400 kg average tyre load. There is little choice of available caravan models at 800 kg tare or 1,600 kg tare for a tandem axle, thus limiting the proposed tyre specification for caravan use. Further, t he UPTIS® photos from the press releases show 64 spokes per tyre. Each spoke having 13 spring steel elements according to the patent diagrams. To outfit the BOLT requires a staggering 3,328 spring steel elemen ts. This, in an industry extremely sensitive to even a single unnecessary washer. Fortunately, it does not need a spare tyre so avoiding another 832 elements. Notwithstanding, the air pumping action of the knee -shaped spoke should keep the UPTIS® tyre c ool and so extend its service life. Then too, there is scope to provide greater lateral stiffness to the rear tyres for perfect directional control by the Bolt EV. Then there may be scope for a bigger specification for future outfitting , say, GM’s Hummer model . Given the military predilection for this model, t here is the hope for caravans in the foreseeable future . As for eliminating fishtailing altogether ? Routine publication of tyre lateral stiffness by tyre manufacturers would be a good starting po int. Failing that, a run -flat tyre of the 16 type that has stiffened sidewalls might be an option. A comparison of normal tyre with a run -flat tyre is compared in Figure 20: Figure 20 – Cross-section of run-flat tyre (left) compared with normal tyre (right)