Colin Chapman and the Evolution of Lotus Chassis Design
This article is intended to be brief and act as an introduction. It’s an appreciation based on the rapid technical developments within Lotus.
The reputation and International success of Lotus on and off the track was based on the handling and performance. For this reason it’s important to examine how this was achieved .The application of theory to practice, the motivation, conception, inspiration and relativity with peers and rivals.
The article has been written in basic elementary language to permit a first stage overview and to allow students and novices a glimpse at basic principles consistent with the A&R approach using Chapman thinking as an educational tool.
It is also hoped that by giving a thorough set of references students might be prompted to access the best original sources.
The Illustrative Models and Photographs
The subject is not easy to approach because access to working drawings is restricted. Also it’s often difficult to have sight to cars during construction / restoration .For this reason the author has made recourse to models. Many of which have been based on photographs and diagrams only. The author wishes to make clear for this reason there may be inaccuracies but for the purpose of the exercise they are intended to be illustrative in the absence of alternatives. A mannerequin has been placed within the chassis design to show relative scale, seating ergonomics and orientation.
However they do offer the opportunity to be examined 3D and for some, especially students this might be more easily comprehended. The illustrations that accompany this article are based on these models and its hoped they will provide an opportunity to see in one place the evolution of chassis design and an interaction between theory and practice, form and function.
The textbooks quoted in the references give expert details and some drawings.
Designers at Lotus
The tendency is to assume that Chapman was the universal genius at Lotus responsible for all designs. Although he may have had a significant role in the early years this altered later on. To acknowledge the other designers contributions is fair, objective and desirable in the fullest appreciation of the subject. Their inclusion helps inspire future designers and signifies levels of teamwork.
The names of those who have been involved includes:
- Dave Baldwin
- Maurice Phillipee
- Ralph Bellamy
- Martin Ogilvie
- Gerard Ducarouge
- Frank Dernie
- Chris Murphy
- Peter Wright
- Tony Rudd
- Martin Wade
- Mike Cooke
- Ron Hickman
- Len Terry
- Geoff Aldridge
- John Joyce
- Tony Southgate
- “Mac” Mackintosh
- Colin Spooner
- Peter Weston
First Principles, Light Weight Construction
A guiding principle of mechanical efficiency and indeed aircraft construction is lightweight. The reasons are [particularly when applied to a motor car]:
Manoeuvrability- improved handling and road holding – less weight to be moved
Power to weight ratio advantage
Improved acceleration and de-acceleration
Fuel and materials efficiency
Weight reduction forms the most powerful spiral of benefits and can be expressed thus: Reduce weight of chassis permits:
Reduction in engine size and weight
Reduce size brks’ and tyres
Reduce suspension components improve handling
Reduce body weight and volume
Leading to greater fuel economy
Smaller tank; lower weight
Chassis can be redesigned around smaller overall lighter components.
Lightweight construction is also a function of sprung and unsprung weight distribution and its impact on handling.
Consider the evidence in a range of equipment that we have had direct experience of racing bicycle, hand tools, and wheelbarrow and camping equipment.
Theory and Sources of Inspiration
Colin Chapman had a first class introduction to these concepts. This was acquired through his academic training, applied experience and feedback, his experience in the RAF and as pilot. In addition Chapman is known to have read widely and extrapolated and modified existing ideas. His membership of the 750 Motor Club was possibly invaluable along with his immense innate skill as a driver. As we examine each chassis type we will return and look at existing precedent. Chapman was also supported by some very able people, gifted in their own right .An early example is that of Allen brothers and later Frank Costin [see listing above]
The editor also recommends the A&R article on “Icons of the 20C” for further insights to the Chapman methodology.
In particular the Second World War had accelerated technological developments especially in aeronautical engineering. From the time of the R100 airship geodesic design principle had been in used in airframes. The Wellington Bomber [by Barnes-Wallace] was a spectacular example. The Warren truss type construction was used in the Hurricane. Airframes were also moving towards monocoque fuselage.
The talent of Chapman was the ability to mutate and extrapolate some of these principles into the motorcar and use experts to help him focus and deliver practical outcomes.
Although the application of aerodynamics in flight and the motorcar frequently differ Chapman was willing to borrow what was applicable and this allowed him to explore ground effect that in turn would interrelate with chassis design etc.
Since Chapman’s death the Lotus has had great success applying the fundamental principles especially in the Elise range.
We should not overlook that weight saving is also a fundamental ingredient of green thinking. Saving energy and materials in construction and the energy required in use.
The Most Elementary Type Chassis/ “A” or Ladder Frame
Car manufacturers and designers are aware of mechanical efficiency. However they are primarily concerned with resolving other considerations into a commercial package.
In the pre Second World War era these were mainly:
Simplicity in manufacture and assembly
Low production and resultant sale price
Reparability. Serviceability and its impact on insurance
Utility of meeting customer requirements e.g. handling may not be first consideration.
The most basic chassis concept of the pre war era was the “A” frame or ladder chassis lay out. [See model illustration]
This is an elementary platform upon which all the necessary mechanical components can be mounted. It has significant shortcomings primarily that the chassis is not rigid enough to provide reliable and accurate steering.
Further more basic chassis offered opportunities for competition such as the 750 Motor Club where a standard chassis reduced costs, made the sport democratic and affordable and possible made for close intense racing where skill was emphasised over technology.
The Improved Ladder Frame: The Lotus Trials Cars and the Mk.III
Having developed an interest in competitive motor sport Colin Chapman sought how to find advantage and improvement. In many branches of sport specifications required a proprietary chassis and scrutineering was enforced to achieve fairness and the objectives of affordability as mentioned above.
Chapman himself at this stage was on a modest budget but his desire to win combined with his application of theory into practice brought out the best of his sense of creativity, innovation, improvisation and interpretation of rules.
Chapman took the basic “A” frame [see model illustration] and started to adapt. The editor recommends the standard textbooks for fuller descriptions. Only a brief résumé will be given here.
The Lotus Mk.I 
Colin constructed a car to compete in trials based on the Austin Seven saloon chassis. The chassis was boxed in [i.e. open “U” channel closed for extra rigidity. The body was constructed of aluminium-skinned plywood. A form of drop down side was adopted to increase strength left by full opening doors. An arrangements of three bulkheads was adopted.
Some of the success of this car was attributed to additional mechanical alterations to improve handling.
The Lotus Mk.II 
This was a trials / racing special again based on the Austin Seven chassis. It was developed and improved with tubular bracing. Chapman also modified the suspension and a Ford engine was fitted.
The Lotus Mk.III. 
The editor has considerable interest in the Mk.III and it will feature shortly in a major article.
The Mk.III was track car. It was built to race in the 750 Motor Club events and followed a different form and function [not to mention regulations] to the trials cars.
Chapman and the Allen brothers extensively developed the standard Austin chassis almost to the point of being a space frame. The rigidity they introduced displayed theoretical thinking. It is an essay in extracting and interpreting the rulebook to limits of legal acceptability and perhaps in some respects beyond. The Allen brothers provided enormous help and resources: material, financial, technical skill, premises along with friendship and good will.
Brief details of the chassis:
Boxed Austin Seven a frame with replacement cross members.
Retained standard chassis and 81” wheel base to meet regulations
Bracing around the engine on triangulation principle.
Rear chassis extension to accept petrol tank, rear axle and suspension mounting.
Chassis modifications to support improved suspension arrangement
The Lotus Mk.IV 
Constructed as dual-purpose road and trials car. This car had some similarities with the Mk.II and still retained an Austin Seven chassis. Combinations of Ford and Austin mechanical components were used. The body was constructed in aluminium sheet.
The Space Frame Tube Chassis.
Significant Lotus with Space frame chassis:
Sports / racing: 6, Seven 8,9,10,11,15,17,19
Single Seat racing car: 12,16,59,61
[Note that these tube chassis incorporated both front and rear mounted engines.]
The space frame tube chassis was not totally new when Chapman designed the Mk.VI.
The construction had been used in the aircraft industry making fuselages etc. It had also been the principle on which bridges were built. Other manufactures had adopted this method including Cististalia, Mercedes-Benz and Jaguar [“C” Type] .In the 1930’s Buckminster Fuller designed a car called the Dymaxion which attempted to extrapolate airframe technology. [See article on Industrial Designer.] This was based on principles of triangulation.
The Wellington bomber by Barnes Wallace was a great success of the Second World War and this too used space frame construction techniques.
Buckler was another British specialist car manufacture that was working in tube design concurrently.
Part of Colin Chapman’s genius was to manage theory into direct practice often with considerable help from friends and specialists.
The Lotus Mk.VI [see model chassis illustration]
This is his first Lotus essay in space frame construction and possibly was conceived directly to challenge in the 1172 Formula. This in many respects was a variant on the Austin 750 principle of affordable racing around inexpensive and available parts. Chapman’s design was efficient and relatively affordable for the era and had the advantage of offering a dual road / racecar. Of course it was front engined and used a variety of engines and capacities.
The success of the Mk.VI might be attributed to:
Its theoretical structural principles
Its utter practicality utilizing Ford components dating from the 1930’s.
Its specification meeting the 1172 Formula but is flexibility to accept other engines and race in other classes.
Its relative inexpensive [see our article on Price Relativity to fully understand this. E.g. a constructed complete car in the early 1950’s might cost £400 -500
Rugged reliability and serviceability
The high quality and light weight aluminium bodies by Williams and Pritchard [also see A&R articles]
Tube Space from chassis needs skilled workmen to construct. They are time consuming and considerable patience is required.
Once again the Allen brothers and family provided moral, financial, technical support to ensure the prototype Mk.VI was constructed to a very high standard.
The space frame chassis principle delivered the theoretical requirements of lightweight and rigidity. The Chapman design was quite a work of art especially when compared with the proprietary Ford Specials of the era that retained the production Ford chassis.
Readers are invited to attempt to design their own chassis and bodywork to see if they can improve or simplify the Chapman design. It is extremely difficult because of the thoroughness with which Chapman sought to integrate all elements within a totality. Furthermore the Ford components are utilised, improved and lightened in the process.
The first prototype Mk.VI is thought of as XML 6 with the Ford Consul engine. In hindsight it is considered slightly over engineered and may have been heavier than absolutely necessary. The possible explanations are:
Larger more powerful engines [class of racing was contemplated] and to give owners flexibility in choice.
Practicality in ration Britain might have reduced supplies of tube. Or chassis jig may have been made to accept standard size
Element of caution and desire to enhance reputation reduce risk.
It is well documented just how successful the MK.VI was. It’s the editor’s contention that the 100 or so cars built both commercially [providing significant working capital] and competitively established Colin Chapman and Lotus. The most successful of the Mk.VI is thought to be UPE 9 [and this will be the source of a future detailed article]
Thereafter very quickly in rapid succession Colin Chapman refined, evolved and perfected the space frame chassis. These were developed in conjunction with the aerodynamic bodies .The Mk.VIII. IX, X and Eleven
[See chassis model illustrations of the Mk. VIII and Eleven]
The Mk.VIII 
This chassis is considered the most theoretically perfect but at the price of practicality and it suffered in consequence. It was very simple, extremely light and stiff .it was welded up from 18&20 gauge tube. It comprises two sections afore and aft of central bulkhead. It’s believed that only 19 pieces are used and weight was approximately 21lbs. by reference to the model it can be seen that all structural pieces are straight and triangulated.
Chapman was a realist and self-critical each design was improved and he moved on incorporating improvements.
With these designs Chapman dominated the sport until the advent of the Lola.
All the major textbooks listed in the bibliography provide fuller explanations, drawings and diagrams. The tube space frame chassis requires careful calculation to maximise its advantages. The textbooks suggest how these might be undertaken. Peter Ross is amongst the best for practical directly related illustration and context.
The Eleven  [see chassis model illustration]
The Eleven was a logical development of the Mk.IX and the package was possibly one of the greatest with its combination of advanced chassis and aerodynamic body with input from Frank Costin. It sold in considerable numbers and competed successfully internationally including Le Mans and at British Club level. With approximately 270 models sold across a three-model range.
The Eleven chassis was properly stressed i.e. using term relating to calculations resulting in a multi-tubular triangulated space frame chassis using 1” and ¾” tubes of 18 or 20 swg thickness. In photographs it is self-evident the minimum of tubing deployed. A stressed aluminium prop shaft tunnel and floor contributed to rigidity.
The whole concept was a unified aesthetically pleasing practical proposition with both front and rear body sections pivoted for ease of access.
The Lotus Seven. 
Little needs to be said about this car. Its well known that it was development and simplification of the Eleven.
The editor calls attention to the essential correctness of the space frame design by reference to the Caterham Seven and how they have remained faithful to the concept. [Photographs show the current generation and a prototype chassis]
It s worth noting that the series IV Seven used a modified chassis possibly conceived with production economics in mind.
Chapman persisted with the front engine tube chassis in the Type 12 &16 FI cars up to 1958 and also the 15 and 17 sports racing cars.
The tube space frame chassis had become standard competition practice from the early 1950’s. The significant change in the latter part of the decade was the move to mid and rear engine. [It’s interesting to contemplate if Chapman had participated in F500 if rear engine would have appeared sooner.]
Chapman’s first rear engine car was the Type18. Following the Cooper layout Chapman produced the Lotus 19 and 23 [see editors scale model photographs of the 19] also refer to textbooks. Later Lotus single seat models with a space frame included the 20,21, 22 and 24.
The Chapman concept has virtually been the basis of kit car construction up to the present day with the various Lotus Seven interpretations. The construction method is relatively simple and inexpensive compared to composites.
The Nineteen  [see chassis model illustration]
The three-section space frame was similar to the 18 but obviously adapted for a two-seater sports racing car. [Appendix C] the front and rear bullheads are FI type .the central scuttle hoop is tubular and perforated steel structure designed to eliminate diagonal bracing. This element was in true Lotus fashion providing multiple use and mounting for various components. A further rear bulkhead provides additional mounting points etc.
Complete with all brackets the chassis weighs approximately 70lbs.
The bodywork adopted was mainly glass fibre with two removable panels front and rear.
Curb weight with the rear mounted Coventry climax engine is estimated at 11cwt.
The Monococque Theoretical Description.
The definition of monocoque is derived from a shell. The easiest and possibly most perfect example is an eggshell.
It possesses enormous strength to weight ratios but these are dependent upon the continuous unbroken / interrupted “skin” that supports or distributes loads. The dome constructions of certain roof types have similar properties.
However terminology and practical applications often get blurred. For this reason the editor suggests readers examine carefully the range of diagrams, drawings, cross sections and photographs of models and written descriptions given in the reference books.
The monocoque has its precedent in history and early examples included: Voisin GP car c 1923, Lancia Lambarda c 1923, Traction Avant c 1934, Morris Minor 1948 and the “D” Type Jaguar possessed a central section of monocoque construction.
The aircraft industry has widely adopted it because of its inherent advantages in allowing internal volume [carrying capacity and its strength to weight ratio]. Airframes might have been constructed in this fashion from as early as 1916 and it’s believed the Douglas DC3 was constructed on this principle.
The editor appreciates that students might have some difficulty in comprehending and visualising the concept especially when two very different almost opposing construction methods are used. The illustrations might be of assistance associated wide reading to increase familiarity. From which there is an increased appreciation of form function resultant from theoretical concepts.
The monocoque has great inherent advantages but always with a motorcar there are practical considerations. The engine and drive have to be able to be included. These considerations can often compromise a concept [think about the theoretical correctness of the MkVIII but its limitations.]
Overcoming such practical necessities can complicate design or require considerable calculation. The considerations also pan out to production costs, and serviceability.
In the case of Colin Chapman and Lotus we have two contrasting examples of monocoque construction both revealing the depth of analysis and conceptual interpretation of which he was capable.
A. The Lotus Elite. 
It’s difficult to comprehend the ambition, audacity and determination of Chapman to undertake such a complex monocoque construction in 1957 when the company was relatively small both in manpower and capital. In the same year as Lotus launched the Type 12 and Seven Series 1.
It has been suggested there was an overpowering rationale. This might have related to a class of racing that would require volume sales. Do doubt Chapman would have seen the duality and interlinked “rocker” potential between.
Volume sales would advance income for racing investment, produce a car with readily available components that would assist competition success. Success on the track would encourage sales and the initial volume would be justified. Win if you could get it right. It was a big ask.
Simply put: The Elite and homologation v manufacture volume sales and proceeds to racing.
The editor had often wondered what feasibility economics had been undertaken for the Elite but the thought of homologation no doubt overtook other considerations. None of the major mainstream manufacturers were so bold as to contemplate the complexities and risks associated with this constructional method and materials.
The structure of the Elite
The editor has been unable to make a model of the Elite monocoque chassis. The nearest equivalent is the plastic scale models and one of this type has been used to explain the principles.
The Elite was assembled from 3 major mouldings, which in turn involved possibly eight box sections. Metal tubing and plate inserts provided further reinforcement and pick up points.
The Elite was a tour de force not only in structural ingenuity but also aesthetics. It possessed an extremely low cd estimated at approximately 0.29.
To achieve maximum advantage this type of chassis requires considerable calculations in order that strength is placed where needed. Consequently the chassis varied in thickness throughout.
Production complexities and costs were possibly underestimated and the Elite was not a commercial success. There were other inherent weaknesses relating to noise transmission.
B.The Lotus 25  and single seater racing car type. [See chassis model illustration]
The Type 25 revolutionised FI in 1962. It provided Lotus with international success with the 1963 World Championship. Jim Clark was the driver. It may be recorded as one of the greatest racing cars of all time.
The theoretical concepts of the monococque have been noted along with the application in airframes. Chapman suggested his inspiration for the Type 25 was the backbone chassis of the Elan. This is totally consistent with the Chapman methodology of thinking, conceptualisation and extrapolation.
Its possible that on re-examination / analysis or interpretation Chapman concluded that the backbone chassis might function better in expanded rather than a spine. In a flash of inspiration he might have rationalised that the body and chassis might be one piece integrated, simultaneous and this would accord with the monocoque definition of shell. The driver accommodated “within“ not without. Here names and definitions blur. Some engineers refer to the single seat monocoque as a bathtub as the continuous external unbroken shell is impossible whilst engine and drive have to gain entry and exist.
The monocoque chassis is difficult to comprehend from drawings; it helps to visualise a cross section.
The editor has translated the concept with a large diameter tube with additional compartments. In practice the Type 25 chassis comprised of:
Aluminium sheet 16 SWG riveted accurately within a jig and steel cross members.
A rectangular section either side of the driver containing the fuel bags
Lower body half terminating at end of cockpit
Further extension boxes at rear to contain engine
Engine directly bolted to chassis which contributed to rigidity
A rear hoop bridging the chassis and providing location for rear suspension
Channels in underside in underside carried oil, water, hydraulics and electrical systems.
Further hoops amidships for the steering, dashboard and front suspension
Overall torpedo shape with small frontal area [typical of era 0.54 sq.m but just 0.37 for the Type 25.]
Consistent with structure the driver positioned at extreme inclined angle
The lack of tubes made access and maintenance easier for the mechanics.
Lotus single seaters with monococque chassis [various materials]
Types: 25,27,29, 31,33,34,35,38,39,
70,72,73 74,76 77, 78, 79,
80,81,86,87,88,91, 92,93T 94T, 95T, 96 97T, 98T 99T,
100 T, 101,102
The Backbone Chassis
Depending on conceptualisation and interpretation the backbone chassis has some similarities with the monocoque Type 25. For our analysis we will keep it as separate entity.
The backbone chassis has been in existence for some time before Chapman took it up so successfully. It’s believed that some Skoda and Tatra motorcars had backbone chassis [T87 &T111], as on previous occasions the genius was in the adaptation, extrapolation and incorporation in the most appropriate and effective package. Chapman was able to update the concept and make it applicable to the era. Further more it was simple as the Elite had been complex.
Backbone Chassis in Lotus: The Elan  and Lotus family
The practical application.
Possibly due to the complications and financial losses associated with the Elite Chapman was determined to come up with a more practical and production friendly alternative.
Its possible that he was thinking of replacing the Seven and wanted a car that could potentially be mass produced in the vein of the Austin Healey Sprite /MG Midget but with much improved performance and handling. There was an established proven market if the right product could be produced.
His response was the backbone chassis. This would immediately underpin the Elan of 1962, then the Europa and continue through the Lotus model range:
Elite, Elcat, Esprit, Excel until the M100 and the Elise aluminium extrusion chassis.
Evidence confirms that a large diameter tube has greater / improved structural properties. Chapman’s extension / deduction conceived that an “enlarged tube” might constitute a chassis on its own. It would have proven structural qualities, light, reasonably easily manufactured.
Chapman’s backbone chassis comprised a deep rectangular steel section that was folded and welded with stiffening pieces let in. [see photograph of model]
It weighed 75 lbs [cf space frame for the Mk.VI but possessed considerably greater tensional rigidity.
The hollow core also permitted the prop shaft to run through it. At each end the chassis “forked” out into two narrow cross sections cross members. With turrets at the front accepted the engine, gearbox, steering and suspension.
The rear portion located the final drive and rear suspension. A wrap around glass fibre body was relatively easily fixed to the core backbone running centrally through the cockpit.
The Elan M100. 
This model was launched in 1989. There is a small illustration of the chassis in “The Lotus Book”.
Essentially it was an adapted backbone chassis constructed of box section zinc coated steel and tube with body built up in multiple sections with reinforced glass fibre panels and V.A.R.I. moulded floor.
The editor does not have a model of illustration of this chassis at present.
The Aluminium Extrusion: The Elise 
The current generation of Lotus chassis are based on the lightweight structure of epoxy bonded aluminium extrusion. This is constructed with an integral steel roll bar and lightweight steel sub frames.
The chassis works in conjunction with transverse mid engine and rear wheel drive.
This type of chassis has been referred to as bonded aluminium space frame tub.
The chassis is glued and riveted. It’s claimed that the bare chassis weighs approximately 70kg [approximately half the weight of steel equivalent] Torsion rigidity is recorded at 10.133 Nm/degree and is comparable with a BMW Series III saloon.
This very advanced chassis construction was developed with specialist input from Hydro Aluminium Automotive Structure [based Norway] Its believed they may have a plant in Worcester, UK and Ciba Polymers of Switzerland.
The editor has been unable to construct a model of this chassis but would recommend readers look at:
In this brief article the editor has attempted to reveal the evolution of chassis design at Lotus. This is possibly more evolutionary than expressed in the past. The article wished to look in an almost X Ray fashion at the chassis as this component of the car is often the least revealed and yet has contributed so much to the success of Lotus.
The use of chassis models [perhaps with their limitations] is hoped to provide insights that could not be gained elsewhere and if the proposed museum is established accurate full scale working exhibits will be displayed.
The primary function of the museum is not so much historical record but the dissemination of technical fact and engineering problem solving. Interpretation in this context is communicating the methods and means of achieving objectives through design and use of materials.
This article also demonstrates the extent of Colin Chapman’s energy, ambition and entrepreneurial drive. From 1948 and what has become known as the Mk.1 to the present day there has been a rapid succession of innovation, improvisation and inspired conceptual thinking rooted in theoretical concepts and translated through to practical transport. This was achieved with limited resources and the measure of success must be seen in this context. Colin Chapman with all his faults inspired and employed many first class designers and many others made exceptional sacrifices and contributed materially to his success. There were relative failures too. These must be noted and objectively analysed. They too provide a learning opportunity. In particular they demonstrate Chapman’s determination to learn, move on and not be beaten or succumb to ego. Perhaps one of the greatest strengths of the man was to learn, analyse and see opportunities within obstacles or conventional perceived disaster.
To the engineer the chassis it self is a work of art but many of the Lotus have been pieces of extreme aesthetic beauty.
In today world our concern is towards sustainability. It ought be noted that Chapman perhaps more than any other pioneered and promoted light weight high efficiency construction allied to safety through improved handling This aided by aerodynamic design remains the mantra of sustainability in extracting the most from the least resources.
The editors are pleased to note the success of the current generation of Lotus cars is rooted in proven theoretical principles and perhaps more than most super cars manufacturers has an almost unbroken tradition, track record, recognition, reputation for what many see as purity and essential functional “correctness”
Understanding Aircraft Structures.
Mechanics of Flight
The Science of Flight
O G Sutton
Engineer to Win
Race and Rally Source Book
Fundamentals of Vehicle Bodywork
The Construction of Ford Specials
Ford Specials builders Manual
Racing and Sports Car Chassis Design
Costin and Phipps
Racing Car Design and Development
Terry and Baker
Motor Racing Publications 1973
Sports Car Bodywork
Elements of Automobile Engineering
The Sports Car :Its Design and Development
Chapman and Hall 1978
Chapman and Hall 1981
Colin Chapman –Lotus Engineering*
Lotus: The Early Years.
The Lotus Book
Coterie Press 1999
Coterie Press 2002
The Complete History of GP Motor Racing*
Arum press 1997
All books listed are part of the A&R library except marked * Please ask for clarification, extract or book review if it would be of assistance.